100 High-Scoring MCQs on Rotational and Circular Motion (Set - 1) | Class 11 Physics | Unit 5

100 High-Scoring MCQs on Rotational and Circular Motion (Set - 2) | Class 11 Physics | Unit 5

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This post contains 100 carefully selected multiple-choice questions (MCQs) from Unit-5: Circular and Rotational Motion of Class 11 Physics, designed strictly according to the FBISE syllabus. These MCQs include a well-balanced mix of conceptual and numerical problems, making them exam-ready, revision-friendly, and high-scoring.

Whether you are preparing for annual board exams, chapter tests, or competitive entry exams, this collection thoroughly covers all the key concepts and formulas of circular and rotational motion, helping students master the chapter with confidence.

This unit-wise MCQ set includes questions from:

• Angular displacement, velocity, and acceleration
• Equations of angular motion and their applications
• Uniform and non-uniform circular motion
• Centripetal acceleration and centripetal force
• Sources of centripetal force: tension, friction, gravity, and normal force
• Motion on banked curves and the banking angle formula
• Orbital motion of satellites and orbital velocity derivation
• Weightlessness and artificial gravity in satellites
• Moment of inertia and rotational kinetic energy of various bodies
• Torque, angular momentum, and conservation of angular momentum
• Numerical applications combining rotational dynamics and circular motion
• Real-life examples of rotational and circular motion in mechanics

Each MCQ is provided with the correct answer and a clear, concise explanation, helping students strengthen concepts, avoid common mistakes, and solve numerical problems confidently.

Prepare smartly, revise efficiently, and boost your exam score in Unit-5: Circular and Rotational Motion with these 100 high-yield, Exam-style MCQs.

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MCQs No. 1

A particle moving in a circle with uniform speed has:
a. Zero acceleration
b. Tangential acceleration
c. Centripetal acceleration
d. No velocity

The Correct Answer is option c. Centripetal acceleration

Explanation:
Even with constant speed, direction changes continuously, giving centripetal acceleration.

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MCQs No. 2

If a car rounds a circular bend of radius $r$ at speed $v$, the centripetal force is:
a. $mv$ 
b. $mv^2/r$ 
c. $mr/v^2$ 
d. $v^2/mr$ 

The Correct Answer is option b. $mv^2/r$ 

Explanation:
Centripetal force formula is $F_c = mv^2/r$ .

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MCQs No. 3

The linear speed of a body at radius $r$ is $v = r\omega$. If $\omega$ doubles, linear speed:
a. Halves
b. Remains same
c. Doubles
d. Quadruples

The Correct Answer is option c. Doubles

Explanation:
Linear speed is directly proportional to angular velocity.

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MCQs No. 4

Which of the following is a vector quantity?
a. Angular displacement
b. Angular velocity
c. Angular acceleration
d. All of these

The Correct Answer is option d. All of these

Explanation:
All have magnitude and direction along axis of rotation.

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MCQs No. 5

If a car moves in a circle of radius 100 m at speed 20 m/s, centripetal acceleration is:
a. 2 m/s²
b. 4 m/s²
c. 20 m/s²
d. 400 m/s²

The Correct Answer is option b. 4 m/s²

Explanation:
$a_c = v^2/r = 400/100 = 4$ 

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MCQs No. 6

The tangential acceleration of a rotating body depends on:
a. Angular velocity
b. Angular acceleration
c. Moment of inertia
d. Mass

The Correct Answer is option b. Angular acceleration

Explanation:
Tangential acceleration $a_t = r\alpha$

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MCQs No. 7

A satellite orbits Earth in a circle. Its acceleration is:
a. Zero
b. Tangential
c. Centripetal
d. Linear

The Correct Answer is option c. Centripetal

Explanation:
Gravitational force provides centripetal acceleration.

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MCQs No. 8

The linear velocity at the rim of a wheel of radius 0.5 m rotating at 2 rad/s is:
a. 1 m/s
b. 2 m/s
c. 0.25 m/s
d. 4 m/s

The Correct Answer is option a. 1 m/s

Explanation:
 v=rω=0.5×2=1 m/s.

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MCQs No. 9

Angular acceleration is zero when:
a. Torque is applied
b. Angular velocity is constant
c. Moment of inertia is zero
d. Mass is zero

The Correct Answer is option b. Angular velocity is constant

Explanation:
Angular acceleration is the rate of change of angular velocity.

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MCQs No. 10

The horizontal component of normal force on a banked road provides:
a. Frictional force
b. Weight
c. Centripetal force
d. Torque

The Correct Answer is option c. Centripetal force

Explanation:
On a frictionless banked road, centripetal acceleration is due to the horizontal component of normal force.

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MCQs No. 11

Angular momentum of a rotating body is:
a. Iω
b. mω²
c. Iα
d. mr²ω

The Correct Answer is option a. Iω

Explanation:
Angular momentum = moment of inertia × angular velocity.

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MCQs No. 12

The SI unit of torque is:
a. N·m
b. J
c. kg·m²/s²
d. W

The Correct Answer is option a. N·m

Explanation:
Torque = force × perpendicular distance.

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MCQs No. 13

A uniform disc rotates about its axis. Moment of inertia is:
a. MR²
b. ½MR²
c. ⅖MR²
d. ⅓MR²

The Correct Answer is option b. ½MR²

Explanation:
Standard formula for a uniform disc about its center.

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MCQs No. 14

If the speed of a body in circular motion is doubled, centripetal force:
a. Remains same
b. Doubles
c. Quadruples
d. Halves

The Correct Answer is option c. Quadruples

Explanation:
Centripetal force $F_c = mv^2/r$ 

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MCQs No. 15

Which force keeps Moon in orbit?
a. Normal reaction
b. Tension
c. Gravitational
d. Friction

The Correct Answer is option c. Gravitational

Explanation:
Earth’s gravity acts as centripetal force.

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MCQs No. 16

If a body rotates faster, its angular momentum can be increased by:
a. Increasing radius
b. Decreasing radius
c. Decreasing mass
d. Reducing torque

The Correct Answer is option a. Increasing radius

Explanation:
L = Iω; I depends on radius squared.

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MCQs No. 17

The satellite appears stationary relative to Earth if its period is:
a. 12 hours
b. 18 hours
c. 24 hours
d. 36 hours

The Correct Answer is option c. 24 hours

Explanation:
Geostationary satellites revolve once per day.

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MCQs No. 18

Weightlessness in orbit occurs because:
a. Gravity is zero
b. Mass is zero
c. Both satellite and objects accelerate equally
d. Force is large

The Correct Answer is option c. Both satellite and objects accelerate equally

Explanation:
Objects fall freely inside satellite with same acceleration.

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MCQs No. 19

Tangential acceleration is related to:
a. Centripetal force
b. Torque
c. Angular acceleration
d. Gravity

The Correct Answer is option c. Angular acceleration

Explanation:
$a_t = r\alpha$ 

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MCQs No. 20

For a ring of mass M and radius R, moment of inertia about axis through center:
a. 1/2 MR²
b. MR²
c. 2/3 MR²
d. 2/5 MR²

The Correct Answer is option b. MR²

Explanation:
All mass is at distance R from axis.

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MCQs No. 21

Angular velocity vector direction is given by:
a. Left-hand rule
b. Right-hand thumb rule
c. Fleming’s left-hand rule
d. Maxwell’s rule

The Correct Answer is option b. Right-hand thumb rule

Explanation:
Curl fingers along rotation; thumb gives vector direction.

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MCQs No. 22

Centripetal acceleration depends on:
a. Mass and speed
b. Speed and radius
c. Radius only
d. Mass only

The Correct Answer is option b. Speed and radius

Explanation:
$a_c = v^2/r$ 

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MCQs No. 23

Which quantity is scalar?
a. Angular velocity
b. Angular momentum
c. Torque
d. Rotational kinetic energy

The Correct Answer is option d. Rotational kinetic energy

Explanation:
Energy has magnitude only.

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MCQs No. 24

Torque on a body depends on:
a. Force only
b. Lever arm only
c. Force and lever arm
d. Mass

The Correct Answer is option c. Force and lever arm

Explanation:
Torque = F × r

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MCQs No. 25

If a spinning ice skater pulls arms in, angular velocity:
a. Decreases
b. Remains same
c. Increases
d. Becomes zero

The Correct Answer is option c. Increases

Explanation:
Conservation of angular momentum.

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MCQs No. 26

Angular acceleration is produced by:
a. Force
b. Torque
c. Power
d. Work

The Correct Answer is option b. Torque

Explanation:
τ = Iα

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MCQs No. 27

Unit of angular momentum:
a. kg·m²/s
b. kg·m²/s²
c. N·m
d. J

The Correct Answer is option a. kg·m²/s

Explanation:
L = Iω

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MCQs No. 28

A vehicle moves on banked curve. The banking angle depends on:
a. Radius, g, speed
b. Mass, radius, speed
c. Friction only
d. Gravity only

The Correct Answer is option a. Radius, g, speed

Explanation:
tanθ = v²/(rg)

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MCQs No. 29

Centripetal force acts:
a. Along velocity
b. Opposite to velocity
c. Radially inward
d. Tangentially

The Correct Answer is option c. Radially inward

Explanation:
Always toward center.

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MCQs No. 30

Angular acceleration of a body is zero when:
a. Torque applied
b. Angular velocity constant
c. Force applied
d. Velocity zero

The Correct Answer is option b. Angular velocity constant

Explanation:
No change in angular speed.

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MCQs No. 31

If speed of a satellite increases, required centripetal force:
a. Decreases
b. Increases
c. Remains same
d. Zero

The Correct Answer is option b. Increases

Explanation:
Fc = mv²/r

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MCQs No. 32

Centripetal force can be provided by:
a. Tension
b. Friction
c. Gravity
d. All of these

The Correct Answer is option d. All of these

Explanation:
Depending on situation.

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MCQs No. 33

Linear speed at radius r = 2 m, ω = 5 rad/s:
a. 10 m/s
b. 7 m/s
c. 2 m/s
d. 5 m/s

The Correct Answer is option a. 10 m/s

Explanation:
v = rω = 2×5 = 10 m/s

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MCQs No. 34

If torque doubles, angular acceleration:
a. Halves
b. Doubles
c. Same
d. Zero

The Correct Answer is option b. Doubles

Explanation:
α = τ/I

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MCQs No. 35

Which is maximum at rim of wheel?
a. Angular velocity
b. Angular acceleration
c. Linear speed
d. Moment of inertia

The Correct Answer is option c. Linear speed

Explanation:
v = rω

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MCQs No. 36

A satellite in low Earth orbit moves at speed:
a. 2 km/s
b. 8 km/s
c. 15 km/s
d. 1 km/s

The Correct Answer is option b. 8 km/s

Explanation:
Approximate orbital speed.

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MCQs No. 37

Work done by centripetal force is:
a. Maximum
b. Zero
c. Half
d. Constant

The Correct Answer is option b. Zero

Explanation:
Force perpendicular to displacement.

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MCQs No. 38

Unit of moment of inertia:
a. kg·m²
b. N·m
c. J
d. W

The Correct Answer is option a. kg·m²

Explanation:
Rotational analogue of mass.

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MCQs No. 39

Torque is zero when:
a. Force along radius
b. Force perpendicular
c. Force applied
d. Axis through center

The Correct Answer is option a. Force along radius

Explanation:
Lever arm = 0, τ = F×r

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MCQs No. 40

Which of these depends on mass distribution?
a. Angular velocity
b. Torque
c. Moment of inertia
d. Linear speed

The Correct Answer is option c. Moment of inertia

Explanation:
I = Σ m r²

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MCQs No. 41

Rotational kinetic energy of a body:
a. ½mv²
b. ½Iω²
c. Iα²
d. mgh

The Correct Answer is option b. ½Iω²

Explanation:
Rotational analogue of linear KE.

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MCQs No. 42

For uniform circular motion, which is constant?
a. Speed
b. Velocity
c. Acceleration
d. Force

The Correct Answer is option a. Speed

Explanation:
Only magnitude of velocity remains constant.

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MCQs No. 43

If a wheel rotates with angular velocity ω, tangential speed at radius r is:
a. ω/r
b. rω
c. r/ω
d. ω²r

The Correct Answer is option b. rω

Explanation:
v = rω

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MCQs No. 44

If mass of a particle doubles in circular motion, centripetal force:
a. Halves
b. Doubles
c. Unchanged
d. Quadruples

The Correct Answer is option b. Doubles

Explanation:
Fc ∝ m

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MCQs No. 45

Centripetal acceleration depends on:
a. Mass only
b. Velocity only
c. Radius only
d. Velocity and radius

The Correct Answer is option d. Velocity and radius

Explanation:
$a_c = v²/r$

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MCQs No. 46

The maximum speed a car can travel on flat circular road without skidding depends on:
a. Mass of car
b. Friction coefficient
c. Engine power
d. Height of car

The Correct Answer is option b. Friction coefficient

Explanation:
Friction provides centripetal force.

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MCQs No. 47

A body moving in a circle experiences:
a. Tangential acceleration only
b. Centripetal acceleration only
c. Both tangential and radial acceleration
d. No acceleration

The Correct Answer is option b. Centripetal acceleration only

Explanation:
For uniform circular motion.

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MCQs No. 48

Unit of angular velocity:
a. m/s
b. rad/s
c. rad/s²
d. m²/s²

The Correct Answer is option b. rad/s

Explanation:
Rate of change of angular displacement.

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MCQs No. 49

The tangential component of acceleration depends on:
a. Mass
b. Force
c. Angular acceleration
d. Radius

The Correct Answer is option c. Angular acceleration

Explanation:
$a_t = rα$ 

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MCQs No. 50

If a particle moves in a circular path with decreasing speed, which statement is correct?

a. Angular momentum remains constant
b. Particle moves in a spiral path
c. Direction of angular momentum remains constant
d. Angular momentum becomes zero

The Correct Answer is option c. Direction of angular momentum remains constant

Explanation:
Magnitude of angular momentum changes due to change in speed, but its direction remains fixed if the plane of motion does not change.

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MCQs No. 51

What will be the velocity vector of a particle moving in a circle describing equal angles in equal times?

a. Changes in direction
b. Remains constant
c. Changes in magnitude
d. Change both in direction and magnitude

The Correct Answer is option a. Changes in direction

Explanation:
The given motion represents uniform circular motion. In such motion, the magnitude of velocity remains constant but its direction changes continuously, producing centripetal acceleration.

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MCQs No. 52

The angular speed in rad/hour for daily rotation of the Earth is:

a.  $2\pi$
b. $4\pi$

c. $\dfrac{\pi}{6}$

d. $\dfrac{\pi}{12}$

The Correct Answer is option d. $\dfrac{\pi}{12}$

Explanation:
Earth completes one revolution ( $2\pi$ rad ) in 24 hours:

$$\omega=\frac{2\pi}{24}=\frac{\pi}{12}\ \text{rad/hour}$$

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MCQs No. 53

The angular velocity of a body moving with constant speed $v$ in a circle of radius $r$ is:

a. $\dfrac{v^2}{r}$

b. $rv$ 

c. $\dfrac{v}{r}$

d. $\dfrac{r}{v}$

The Correct Answer is option c. $\dfrac{v}{r}$

Explanation:
Using the relation $v=r\omega$ , we get:

$$\omega=\frac{v}{r}$$

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MCQs No. 54

Consider a satellite moving around the Earth. Which statement is WRONG?

a. It is a freely falling body
b. It suffers no acceleration
c. It moves with constant speed
d. Its angular momentum remains constant

The Correct Answer is option b. It suffers no acceleration

Explanation:
The satellite continuously changes direction, hence it has centripetal acceleration toward the Earth.

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MCQs No. 55

If a particle moves with constant angular velocity in a circle, which quantity is conserved?

a. Momentum
b. Energy
c. Both energy and momentum
d. None

The Correct Answer is option b. Energy

Explanation:
The direction of linear momentum changes continuously, so it is not conserved. However, mechanical energy remains constant.

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MCQs No. 56

The direction of angular velocity vector is along:

a. Tangent to the path
b. Inward radius
c. Outward radius
d. Axis of rotation

The Correct Answer is option d. Axis of rotation

Explanation:
Angular velocity is an axial vector whose direction is given by the right-hand rule.

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MCQs No. 57

The angular speed of a flywheel making 120 rev/min is:

a. $2\pi\ \text{rad/s}$ 
b. $4\pi^2\ \text{rad/s}$ 
c. $\pi\ \text{rad/s}$ 
d. $4\pi \text{ rad/s }$

The Correct Answer is option d. $4\pi\ \text{rad/s}$ 

Explanation:

$$\omega=\frac{120\times2\pi}{60}=4\pi\ \text{rad/s}$$ 

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MCQs No. 58

If the linear speed of a particle is doubled and its angular speed is halved, the centripetal acceleration will:

a. Become four times
b. Double
c. Halve
d. Remain unchanged

The Correct Answer is option d. Remain unchanged

Explanation:

$$a=v\omega \Rightarrow a'=(2v)\left(\frac{\omega}{2}\right)=v\omega$$ 

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MCQs No. 59

The angular speed of the second hand of a clock is:

a. $\dfrac{\pi}{30}\ \text{rad/s}$ 

b. $2\pi\ \text{rad/s}$ 

c. $\pi\ \text{rad/s}$ 

d. $\dfrac{60}{\pi}\ \text{rad/s}$ 

The Correct Answer is option a. $\dfrac{\pi}{30}\ \text{rad/s}$ 

Explanation:
The second hand completes one revolution in 60 s:

$$\omega=\frac{2\pi}{60}=\frac{\pi}{30}\ \text{rad/s}$$ 

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MCQs No. 60

A particle of mass 2 kg moves in a circle of radius 1 m with angular speed $2\pi$ rad/s. The centripetal force is:

a. $4\pi$ N
b. $8\pi^2$ N
c. $4\pi^2$ N
d. $8\pi$ N

The Correct Answer is option b. $8\pi^2$ N

Explanation:

$$F=mr\omega^2=2\times1\times(2\pi)^2=8\pi^2\ \text{N}$$ 

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MCQs No. 61

When a lift moves uniformly downward, the apparent weight of a person inside is:

a. Greater than real weight
b. Less than real weight
c. Equal to real weight
d. Zero

The Correct Answer is option c. Equal to real weight

Explanation:
Uniform motion means zero acceleration, hence net force is zero.

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MCQs No. 62

The dimensions of moment of inertia are:

a. $[ML^2]$ 
b. $[ML^2T^0]$ 
c. Both (a) and (b)
d. None

The Correct Answer is option c. Both (a) and (b)

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MCQs No. 63

A particle in uniform circular motion — choose the WRONG statement:

a. Speed is constant
b. Acceleration is perpendicular to velocity
c. Acceleration is uniform
d. Velocity is variable

The Correct Answer is option c. Acceleration is uniform

Explanation:
The magnitude of centripetal acceleration is constant, but its direction changes, so acceleration is not uniform.

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MCQs No. 64

As the height of a satellite’s orbit increases, its orbital speed:

a. Increases
b. Decreases
c. Remains constant
d. Becomes zero

The Correct Answer is option b. Decreases

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MCQs No. 65

When ice at the Earth’s poles melts, the duration of the day:

a. Decreases
b. Increases
c. Remains same
d. Depends on melting rate

The Correct Answer is option b. Increases

Explanation:
Moment of inertia of Earth increases, angular speed decreases, hence time period increases.

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MCQs No. 66

In rotational motion of a rigid body, all particles have:

a. Same linear and angular velocity
b. Same linear but different angular velocity
c. Same angular but different linear velocity
d. Different linear and angular velocity

The Correct Answer is option c. Same angular but different linear velocity

Explanation:
In rotational motion, all particles of a rigid body rotate with the same angular velocity about the axis of rotation. However, the linear velocity varies depending on the distance from the axis ($v = r\omega$).

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MCQs No. 67

Angular momentum of a body remains conserved if:

a. Net force is zero
b. Net pressure is zero
c. Net torque is applied
d. Net external torque is zero

The Correct Answer is option d. Net external torque is zero

From the law of conservation of angular momentum:

$$\vec{L} = \text{constant if } \vec{\tau}_{\text{ext}} = 0$$

If no external torque acts on a body, its angular momentum remains unchanged.

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MCQs No. 68

A disc and a hoop of the same mass roll down an inclined plane. Which reaches first?

a. Hoop
b. Disc
c. Both together
d. None

The Correct Answer is option b. Disc

Explanation:
The disc has a smaller moment of inertia ($I = \frac{1}{2}MR^2$ ) than the hoop ($I = MR^2$ ).
Less rotational inertia → more acceleration → disc reaches the bottom first.

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MCQs No. 69

Moment of inertia of a solid sphere about its diameter is:

a. $MR^2$ 

b. $\frac{1}{2}MR^2$ 

c. $\frac{2}{5}MR^2$ 

d. $\frac{1}{2}MR$ 

The Correct Answer is option c. $\frac{2}{5}MR^2$ 

Explanation:
For a solid sphere, the standard formula for moment of inertia about its diameter is:

$$I = \frac{2}{5}MR^2$$ 

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MCQs No. 70

Which physical quantity produces angular acceleration?

a. Force
b. Power
c. Torque
d. Energy

The Correct Answer is option c. Torque

Explanation:
Angular acceleration is caused by torque ($\tau$), similar to how linear acceleration is caused by force:

$$\alpha = \frac{\tau}{I}$$

Where $\mathrm{I\; is\; the\; moment\; of\; inertia\; of\; the\; body.}$

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MCQs No. 71

A particle moves in a circular path with decreasing speed. Choose the correct statement:

a. Angular momentum remains constant
b. Particle moves in a spiral path
c. The direction of angular momentum remains constant
d. Angular momentum becomes zero

The Correct Answer is option c. The direction of angular momentum remains constant

Explanation:
Although the magnitude of angular momentum changes, its direction remains fixed as long as the plane and sense of rotation do not change.

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MCQs No. 72

The angular momentum of a moving body remains constant if:

a. Net external force is applied
b. Net pressure is applied
c. Net external torque is applied
d. Net external torque is zero

The Correct Answer is option d. Net external torque is zero

Explanation:
According to the law of conservation of angular momentum, angular momentum remains constant when:

$$\tau = \frac{dL}{dt} = 0$$

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MCQs No. 73

A raw egg and a hard-boiled egg are spun on a table with the same angular speed. The ratio of time taken by them to stop is:

a. = 1
b. < 1
c. > 1
d. None of these

The Correct Answer is option b. < 1

Explanation:
A raw egg has internal motion of liquid causing greater energy dissipation, so it stops earlier than a hard-boiled egg.

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MCQs No. 74

If a sphere is rolling without slipping, the ratio of translational kinetic energy to total kinetic energy is:

a. 7 : 10
b. 2 : 5
c. 10 : 7
d. 5 : 7

The Correct Answer is option d. 5 : 7

Explanation:
For a rolling sphere:

$$KE_{total}=KE_{trans}+KE_{rot}$$$$\Rightarrow \frac{KE_{trans}}{KE_{total}}=\frac{5}{7}$$ 

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MCQs No. 75

Two circular discs A and B have the same thickness. The diameter of A is twice that of B. The moment of inertia of A compared to B is:

a. Twice as large
b. Four times as large
c. Eight times as large
d. Sixteen times as large

The Correct Answer is option d. Sixteen times as large

Explanation:
Moment of inertia of a disc:

$$I \propto R^2$$ 

If diameter doubles → radius doubles → $I$ becomes 4 times, and since mass also increases → total 16 times.

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MCQs No. 76

When a body is taken from the equator to the poles, its weight:

a. Remains constant
b. Increases
c. Decreases
d. Increases at north pole only

The Correct Answer is option b. Increases

Explanation:
Radius of Earth is minimum at poles, so gravitational acceleration $g$ is greater. Since $W=mg$, weight increases.

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MCQs No. 77

If a particle moves in the X-Y plane, the resultant angular momentum has:

a. Only x-component
b. Only y-component
c. Both x and y components
d. Only z-component

The Correct Answer is option d. Only z-component

Explanation:
Angular momentum is perpendicular to the plane of motion, hence along the z-axis.

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MCQs No. 78

Two bodies have moments of inertia $I_1$ and $I_2$ such that $I_1 > I_2$. If their angular momenta are equal, then their rotational energies satisfy:

a. $E_1 > E_2$
b. $E_1 < E_2$
c. $E_1 = E_2$
d. None

The Correct Answer is option b. $E_1 < E_2$

Explanation:
Since:

$$I_1\omega_1 = I_2\omega_2,\quad I_1>I_2 \Rightarrow \omega_1<\omega_2$$$$E=\frac{1}{2}I\omega^2 \Rightarrow E_1<E_2$$

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MCQs No. 79

A sphere cannot roll on:

a. Smooth horizontal surface
b. Rough horizontal surface
c. Smooth inclined surface
d. Rough inclined surface

The Correct Answer is option c. Smooth inclined surface

Explanation:
Rolling requires friction to produce torque. A smooth inclined surface provides no friction.

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MCQs No. 80

A disc and a hoop of the same mass and radius roll down an inclined plane together. Which reaches the bottom first?

a. Hoop
b. Disc
c. Both together
d. None

The Correct Answer is option b. Disc

Explanation:
The disc has smaller moment of inertia, so it accelerates faster.

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MCQs No. 81

A satellite orbits Earth with speed $v$ and radius  $r$. If it loses energy, then:

a.  $v$ decreases, $r$ increases
b. Both  $v$ and  $r$ decrease
c.  $v$ increases,  $r$ decreases
d. Both increase

The Correct Answer is option c.  $v$ increases, $r$ decreases

Explanation:
Total energy:

$$E=-\frac{GMm}{2r}$$

 Loss of energy means smaller radius, hence higher orbital speed.

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MCQs No. 82

The moment of inertia of a solid sphere about its diameter is:

a. $MR^2$ 

b. $\frac{1}{2}MR^2$ 

c. $\frac{2}{5}MR^2$ 

d. None

The Correct Answer is option c. $\frac{2}{5}MR^2$ 

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MCQs No. 83

How many geostationary satellites are required to cover the whole Earth?

a. 4
b. 3
c. 2
d. 1

The Correct Answer is option b. 3

Explanation:
Each satellite covers 120° of Earth’s circumference.

$$3 \times 120^\circ = 360^\circ$$ 

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MCQs No. 84

Linear acceleration $a = r\alpha$  when the angle $\theta$  is:

a. 90°
b. 180°
c. 360°
d. 0°

The Correct Answer is option a. 90°

Explanation:
At $90^\circ$, $\sin\theta = 1$, giving maximum tangential acceleration.

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MCQs No. 85

The critical (orbital) velocity of an artificial satellite near Earth’s surface is:

a. 7.9 m/s
b. 7.9 km/s
c. 80 m/s
d. None

The Correct Answer is option b. 7.9 km/s

​Explanation:

The critical (orbital) velocity is the speed required for a satellite to stay in circular orbit near Earth without falling back.

$$v = \sqrt{\frac{GM}{R}} \approx 7.9 \text{ km/s near Earth's surface}$$

Where $G$ is the gravitational constant, $M$ is Earth's mass, and $R$ is Earth's radius.

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MCQs No. 86

The expression for critical velocity of a satellite is:

a. $v=\sqrt{2gR}$

b. $v=\sqrt{gR}$

c. $v=\frac{gR}{2}$

d. None

The Correct Answer is option b. $v=\sqrt{gR}$

​Explanation:

For a satellite in a circular orbit near Earth:

$$\text{Centripetal force} = \text{Gravitational force} \Rightarrow \frac{mv^2}{R} = mg$$$$v^2 = g R \Rightarrow v = \sqrt{g R}$$

This is the standard formula for orbital velocity near Earth's surface.

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MCQs No. 87

Which physical quantity is responsible for producing angular acceleration?

a. Force
b. Power
c. Torque
d. Energy

The Correct Answer is option c. Torque

Explanation:
Angular acceleration ($\alpha$) is caused by torque ($\tau$) acting on a body:

$$\alpha = \frac{\tau}{I}$$

Where $I$  is the moment of inertia. Force alone causes linear acceleration; torque is the rotational equivalent.

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MCQs No. 38

Angular form of centripetal acceleration is:

a. $r\alpha$ 
b. $rw$ 
c. $rw^2$ 
d. $w^2\mathrm{/}\mathrm{r }$

The Correct Answer is option c. $rw^2$ 

Explanation:

$$a=\frac{v^2}{r},\quad v=r\omega \Rightarrow a=r\omega^2$$ 

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MCQs No. 89

When a lift is moving uniformly from the first floor to the ground floor, which statement is correct for a person inside the lift?

a. Apparent weight is more than real weight
b. Apparent weight is less than real weight
c. Apparent weight is equal to real weight
d. Apparent weight becomes zero

The Correct Answer is option c. Apparent weight is equal to real weight

Explanation:
Uniform motion means zero acceleration. Hence net force on the person is zero and apparent weight equals real weight.

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MCQs No. 90

When a lift moves downward from the first floor to the ground floor, which of the following is true?

a. Apparent weight is always more than real weight
b. Apparent weight is always less than real weight
c. Apparent weight is always equal to real weight
d. All are possible

The Correct Answer is option d. All are possible

Explanation:
If the lift moves downward with:

• Increasing speed → apparent weight decreases

• Decreasing speed → apparent weight increases

• Constant speed → apparent weight equals real weight

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MCQs No. 91

As the height of a satellite’s orbit increases, its orbital speed:

a. Increases
b. Decreases
c. Remains the same
d. Becomes zero

The Correct Answer is option b. Decreases

Explanation:
Orbital speed:

$$v=\sqrt{\frac{GM}{r}}$$

As orbital radius $r$ increases, speed decreases.

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MCQs No. 92

Two satellites $S_1$ and $S_2$ are orbiting the Earth at different heights. Which statement is correct?

a. Potential energies of both satellites are equal
b. Kinetic energies of both satellites are equal
c. Kinetic energy of $S_1$ is four times that of $S_2$
d. None of the above

The Correct Answer is option d. None of the above

Explanation:
Potential and kinetic energies of satellites depend on orbital radius, so they cannot be equal unless radii are equal.

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MCQs No. 93

If two rotating bodies have moments of inertia $I_1$ and $I_2$ $(I_1 > I_2)$ and equal angular momentum, then their rotational energies satisfy:

a. $E_1 > E_2$
b. $E_1 < E_2$
c. $E_1 = E_2$
d. None

The Correct Answer is option b. $E_1 < E_2$

Explanation:
For equal angular momentum:

$$I_1\omega_1 = I_2\omega_2$$

Since $I_1 > I_2$, therefore $\omega_1 < \omega_2$ and

$$E=\frac{1}{2}I\omega^2 \Rightarrow E_1 < E_2$$

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MCQs No. 94

When ice at the poles melts and spreads towards the equator, the duration of the day:

a. Decreases
b. Increases
c. Remains same
d. May increase or decrease

The Correct Answer is option b. Increases

Explanation:
Melting ice increases the moment of inertia of Earth. With no external torque:

$$L=I\omega=\text{constant}$$

 Increase in $I$ causes decrease in $\omega$, hence time period increases.

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MCQs No. 95

A particle moves in a circle of radius 2 m with uniform speed 4 m/s. Its centripetal acceleration is:

a. 2 m/s²
b. 4 m/s²
c. 8 m/s²
d. 16 m/s²

The Correct Answer is option c. 8 m/s²

Explanation:
Centripetal acceleration:

$$a_c = \frac{v^2}{r} = \frac{4^2}{2} = \frac{16}{2} = 8 \text{ m/s²}$$ 

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MCQs No. 96

A car moves around a circular track of radius 50 m with speed 10 m/s. The centripetal force acting on a 1000 kg car is:

a. 1000 N
b. 2000 N
c. 2000 N
d. 2000 N

The Correct Answer is option b. 2000 N

Explanation:
Centripetal force depends on mass, speed, and radius:${\mathrm{<br>}}_{}$

$$F_c=\frac{m{v}^2}{r}=\frac{1000\times {10}^2}{50}=\frac{100000}{50}=2000\text{ N}$$

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MCQs No. 97

A wheel rotates with angular velocity 10 rad/s. The point at radius 0.5 m has linear speed:

a. 5 m/s  
b. 10 m/s
c. 2 m/s
d. 20 m/s

The Correct Answer is option a. 5 m/s

Explanation:
Linear velocity $v = r\omega = 0.5 \times 10 = 5 \text{ m/s}$ 

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MCQs No. 98

A satellite orbits Earth in a circular orbit at a height much smaller than Earth’s radius. If the radius doubles, the orbital speed becomes:

a. Half
b. $\frac{1}{\sqrt{2}}$ of original 
c. Same
d. Double

The Correct Answer is option b. $\frac{1}{\sqrt{2}}$ of original

Explanation:
Orbital speed: $v = \sqrt{\frac{GM}{r}}$

​
If $r \to 2r$, then $v \to \sqrt{\frac{GM}{2r}} = \frac{v_0}{\sqrt{2}}$

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MCQs No. 99

Two solid spheres of same mass but radii in ratio 2:1 rotate with same angular speed. Ratio of their rotational kinetic energies is:

a. 1:1
b. 4:1
c. 8:1
d. 16:1 

The Correct Answer is option d. 16:1

Explanation:
Moment of inertia of a sphere: $I=\frac{2}{5}M{R}^2$ 

Rotational kinetic energy: $K = \frac{1}{2} I \omega^2 = \frac{1}{2} \cdot \frac{2}{5} M R^2 \omega^2 = \frac{1}{5} M R^2 \omega^2$

${\mathrm{}}^{}$

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MCQs No. 100

A flywheel of moment of inertia 5 kg·m² rotates with angular speed 10 rad/s. Its rotational kinetic energy is:

a. 50 J
b. 100 J  
c. 250 J
d. 500 J

The Correct Answer is option b. 250 J

Explanation:
Rotational kinetic energy:

$$K = \frac{1}{2} I \omega^2 = \frac{1}{2} \cdot 5 \cdot 10^2 = 2.5 \cdot 100 = 250 \text{ J}$$