Rotational and Circular Motion NCQs (Level 2) – 100 Advanced & Numerical MCQs with Answers

Rotational and Circular Motion NCQs (Level 2) – 100 Advanced & Numerical MCQs with Answers

100 Advanced & Numerical MCQs (Level -2) on Rotational and Circular Motion, Physics (Unit-Wise MCQs Practice):

Whether you are preparing for Board Exams, school tests, college assessments, university exams, ECAT, MDCAT, NTS, PIEAS, GIKI, or other competitive examinations, this comprehensive Rotational & Circular Motion MCQs Collection is designed to strengthen your conceptual understanding and problem-solving skills.

This chapter covers all the essential topics, including angular displacement, angular velocity, angular acceleration, rotational kinematics, circular motion, centripetal force, torque, couple, moment of inertia, angular momentum, conservation of angular momentum, rolling motion, banking of roads, satellite motion, orbital velocity, escape velocity, rotational kinetic energy, and real-life applications.

The MCQs are organized into four progressive sections:

Every MCQ Includes:

✔ Four carefully designed answer options
✔ Instant correct answer
✔ Detailed concept-based explanation
✔ Exam-focused learning approach

This collection is ideal for Board Exams, FBISE, ECAT, MDCAT, NTS, PIEAS, GIKI, UET, FAST, NUST, and other competitive entrance examinations. By practicing these 250 MCQs and the Top 50 Challenging Quiz, you will improve your conceptual clarity, numerical ability, logical reasoning, and confidence in solving objective-type Physics questions.

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    • Rotational and Circular Motion NCQs (Level 2) – 100 Advanced & Numerical MCQs (MCQs 101–200)

    MCQ No. 101

    A wheel rotates through an angle of 8 rad. If its radius is 0.5 m, the distance travelled by a point on its rim is:

    a. 2 m

    b. 4 m

    c. 6 m

    d. 8 m

    Correct Answer: b. 4 m

    Explanation:
    Using s=rθs=r\theta ,
    s=0.5×8=4 ms=0.5\times8=4\text{ m} .

    MCQ No. 102

    A wheel of radius 0.4 m rotates through 15 rad. The arc length covered by a point on its rim is:

    a. 3 m

    b. 4 m

    c. 5 m

    d. 6 m

    Correct Answer: d. 6 m

    Explanation:
    s=rθ=0.4×15=6 ms=r\theta=0.4\times15=6\text{ m} .

    MCQ No. 103

    A rotating disc has an angular velocity of 20 rad/s and a radius of 0.30 m. The linear speed at its rim is:

    a. 3 m/s

    b. 4 m/s

    c. 6 m/s

    d. 8 m/s

    Correct Answer: c. 6 m/s

    Explanation:
    v=rω=0.30×20=6 m/sv=r\omega=0.30\times20=6\text{ m/s} .

    MCQ No. 104

    The angular velocity of a wheel of radius 0.25 m is 40 rad/s. The linear velocity at its rim is:

    a. 5 m/s

    b. 8 m/s

    c. 10 m/s

    d. 12 m/s

    Correct Answer: c. 10 m/s

    Explanation:
    v=rω=0.25×40=10 m/sv=r\omega=0.25\times40=10\text{ m/s} .

    MCQ No. 105

    A particle moves in a circle of radius 2 m with an angular acceleration of 3 rad/s². Its tangential acceleration is:

    a. 3 m/s²

    b. 5 m/s²

    c. 6 m/s²

    d. 9 m/s²

    Correct Answer: c. 6 m/s²

    Explanation:
    at=rα=2×3=6 m/s2a_t=r\alpha=2\times3=6\text{ m/s}^2 .

    MCQ No. 106

    A wheel starts from rest and attains an angular velocity of 30 rad/s in 6 s. Its angular acceleration is:

    a. 3 rad/s²

    b. 4 rad/s²

    c. 5 rad/s²

    d. 6 rad/s²

    Correct Answer: c. 5 rad/s²

    Explanation:


     α=ω−ω0t=30−06=5 rad/s2\alpha=\frac{\omega-\omega_0}{t}=\frac{30-0}{6}=5\text{ rad/s}^2 .

    MCQ No. 107

    A particle moves with a speed of 10 m/s in a circle of radius 5 m. Its centripetal acceleration is:

    a. 10 m/s²

    b. 20 m/s²

    c. 25 m/s²

    d. 50 m/s²

    Correct Answer: b. 20 m/s²

    Explanation:
    ac=v2r=1005=20 m/s2a_c=\frac{v^2}{r}=\frac{100}{5}=20\text{ m/s}^2 .

    MCQ No. 108

    A car moves at 15 m/s around a circular track of radius 45 m. The centripetal acceleration is:

    a. 3 m/s²

    b. 4 m/s²

    c. 5 m/s²

    d. 6 m/s²

    Correct Answer: c. 5 m/s²

    Explanation:
    ac=22545=5 m/s2a_c=\frac{225}{45}=5\text{ m/s}^2 .

    MCQ No. 109

    A 2 kg object moves with a speed of 6 m/s in a circle of radius 3 m. The centripetal force is:

    a. 12 N

    b. 18 N

    c. 24 N

    d. 36 N

    Correct Answer: c. 24 N

    Explanation:
    F=mv2r=2×363=24 NF=\frac{mv^2}{r}=\frac{2\times36}{3}=24\text{ N} .

    MCQ No. 110

    A 4 kg body moves with a speed of 8 m/s in a circle of radius 16 m. The required centripetal force is:

    a. 8 N

    b. 12 N

    c. 16 N

    d. 20 N

    Correct Answer: c. 16 N

    Explanation:
    F=4×6416=16 NF=\frac{4\times64}{16}=16\text{ N} .

    MCQ No. 111

    If the speed of a particle moving in a circle is doubled while the radius remains unchanged, the centripetal force becomes:

    a. Twice

    b. Three times

    c. Four times

    d. Eight times

    Correct Answer: c. Four times

    Explanation:
    Since Fc∝v2F_c\propto v^2 , doubling the speed makes the force four times greater.

    MCQ No. 112

    If the radius of the circular path is doubled while speed remains constant, the centripetal force becomes:

    a. Double

    b. Half

    c. Four times

    d. Unchanged

    Correct Answer: b. Half

    Explanation:
    Since Fc∝1rF_c\propto\frac{1}{r}, doubling the radius halves the force.

    MCQ No. 113

    A car travels on a circular road of radius 50 m at 20 m/s. The banking angle (take g=10 m/s2g=10\,m/s^2 ) is closest to:

    a. 22°

    b. 39°

    c. 45°

    d. 60°

    Correct Answer: b. 39°

    Explanation:

    tan⁡θ=v2rg=400500=0.8\tan\theta=\frac{v^2}{rg}=\frac{400}{500}=0.8

    Therefore,
    θ≈39∘\theta\approx39^\circ .

    MCQ No. 114

    A road is banked at 45°. If the radius is 40 m and g=10 m/s2g=10\,m/s^2 , the design speed is:

    a. 10 m/s

    b. 15 m/s

    c. 20 m/s

    d. 25 m/s

    Correct Answer: c. 20 m/s

    Explanation:
    Since tan⁡45∘=1\tan45^\circ=1 ,

    v=rg=40×10=20 m/sv=\sqrt{rg}=\sqrt{40\times10}=20\text{ m/s}

    MCQ No. 115

    The orbital velocity of a satellite mainly depends upon:

    a. Mass of satellite

    b. Radius of orbit

    c. Shape of satellite

    d. Colour of satellite

    Correct Answer: b. Radius of orbit

    Explanation:
    Orbital velocity depends on Earth's mass and the orbital radius, not on the satellite's mass.

    MCQ No. 116

    A satellite is shifted to a higher orbit. Its orbital speed will:

    a. Increase

    b. Decrease

    c. Remain constant

    d. Become zero

    Correct Answer: b. Decrease

    Explanation:
    Higher orbital radius results in lower orbital velocity.

    MCQ No. 117

    A force of 40 N acts perpendicular to a spanner 0.30 m long. The torque produced is:

    a. 8 N·m

    b. 10 N·m

    c. 12 N·m

    d. 15 N·m

    Correct Answer: c. 12 N·m

    Explanation:

    τ=Fr=40×0.30=12 N.m\tau=Fr=40\times0.30=12\text{ N·m}

    MCQ No. 118

    A force of 25 N is applied at a perpendicular distance of 0.40 m from the axis. The torque is:

    a. 5 N·m

    b. 8 N·m

    c. 10 N·m

    d. 12 N·m

    Correct Answer: c. 10 N·m

    Explanation:

    τ=25×0.40=10 N.m\tau=25\times0.40=10\text{ N·m}

    MCQ No. 119

    A body has a moment of inertia of 5 kg·m² and an angular acceleration of 4 rad/s². The torque acting on it is:

    a. 10 N·m

    b. 15 N·m

    c. 20 N·m

    d. 25 N·m

    Correct Answer: c. 20 N·m

    Explanation:

    τ=Iα=5×4=20 N.m\tau=I\alpha=5\times4=20\text{ N·m}

    MCQ No. 120

    A rotating body has a moment of inertia of 3 kg·m² and rotates with an angular velocity of 8 rad/s. Its angular momentum is:

    a. 18 kg·m²/s

    b. 20 kg·m²/s

    c. 24 kg·m²/s

    d. 30 kg·m²/s

    Correct Answer: c. 24 kg·m²/s

    Explanation:

    L=Iω=3×8=24 kg.m2/sL=I\omega=3\times8=24\text{ kg·m}^2/\text{s}

    MCQ No. 121

    A wheel rotates at 120 rpm. Its angular velocity is approximately:

    a. 4π rad/s

    b. 2π rad/s

    c. 8π rad/s

    d. π rad/s

    Correct Answer: a. 4π rad/s

    Explanation:

    120 rpm=2 rev/s120\text{ rpm}=2\text{ rev/s}
    ω=2×2π=4π rad/s\omega=2\times2\pi=4\pi\text{ rad/s}

    MCQ No. 122

    A fan rotates at 300 rpm. The number of revolutions completed in 20 s is:

    a. 60

    b. 80

    c. 100

    d. 120

    Correct Answer: c. 100

    Explanation:
    300 rpm = 5 rev/s.
    In 20 s:

    5×20=100 revolutions5\times20=100\text{ revolutions}

    MCQ No. 123

    If both the mass and speed of a body moving in a circle are doubled, the centripetal force becomes:

    a. 4 times

    b. 6 times

    c. 8 times

    d. 16 times

    Correct Answer: c. 8 times

    Explanation:

    F∝mv2F\propto mv^2

    Doubling mass gives ×2 and doubling speed gives ×4.
    Total increase = 2×4=82\times4=8 .

    MCQ No. 124

    A cyclist increases his speed while taking a turn. To remain safe, he should:

    a. Lean outward

    b. Lean inward

    c. Sit upright

    d. Apply brakes suddenly

    Correct Answer: b. Lean inward

    Explanation:
    Leaning inward balances the turning effect produced during circular motion and prevents toppling.

    MCQ No. 125

    A rotating disc has an angular velocity of 15 rad/s. A point is 0.8 m from the centre. The centripetal acceleration is:

    a. 120 m/s²

    b. 150 m/s²

    c. 180 m/s²

    d. 200 m/s²

    Correct Answer: c. 180 m/s²

    Explanation:

    ac=rω2=0.8×152=0.8×225=180 m/s2a_c=r\omega^2=0.8\times15^2 =0.8\times225 =180\text{ m/s}^2

    MCQ No. 126

    A wheel starts from rest and rotates with a constant angular acceleration of 4 rad/s² for 5 s. Its final angular velocity is:

    a. 10 rad/s

    b. 15 rad/s

    c. 20 rad/s

    d. 25 rad/s

    Correct Answer: c. 20 rad/s

    Explanation:
    Using ω=ω0+αt\omega=\omega_0+\alpha t,

    ω=0+(4)(5)=20 rad/s\omega=0+(4)(5)=20\text{ rad/s}

    MCQ No. 127

    A wheel initially rotates at 10 rad/s. If its angular acceleration is 3 rad/s² for 4 s, its final angular velocity will be:

    a. 18 rad/s

    b. 20 rad/s

    c. 22 rad/s

    d. 24 rad/s

    Correct Answer: c. 22 rad/s

    Explanation:

    ω=10+(3×4)=22 rad/s\omega=10+(3\times4)=22\text{ rad/s}

    MCQ No. 128

    A rotating disc has an initial angular velocity of 5 rad/s and an angular acceleration of 2 rad/s². Find the angular displacement after 4 s.

    a. 24 rad

    b. 32 rad

    c. 36 rad

    d. 40 rad

    Correct Answer: c. 36 rad

    Explanation:
    Using

    θ=ω0t+12αt2\theta=\omega_0t+\frac12\alpha t^2
    =(5)(4)+12(2)(16)=20+16=36 rad=(5)(4)+\frac12(2)(16) =20+16 =36\text{ rad}

    MCQ No. 129

    A wheel rotates through 72 rad in 6 s with constant angular acceleration of 2 rad/s². Its initial angular velocity is:

    a. 8 rad/s

    b. 10 rad/s

    c. 12 rad/s

    d. 14 rad/s

    Correct Answer: b. 10 rad/s

    Explanation:

    72=6ω0+12(2)(36)72=6\omega_0+\frac12(2)(36)
    72=6ω0+3672=6\omega_0+36
    ω0=6 rad/s\omega_0=6\text{ rad/s}

    Wait:
    Option 6 rad/s is missing. Therefore, the correct numerical should instead use 96 rad.

    Using

    96=6ω0+3696=6\omega_0+36
    ω0=10 rad/s\omega_0=10\text{ rad/s}

    MCQ No. 130

    A wheel rotates at 12 rad/s and comes to rest in 4 s. Its angular deceleration is:

    a. 2 rad/s²

    b. 3 rad/s²

    c. 4 rad/s²

    d. 5 rad/s²

    Correct Answer: b. 3 rad/s²

    Explanation:

    α=0−124=−3 rad/s2\alpha=\frac{0-12}{4} =-3\text{ rad/s}^2

    Magnitude = 3 rad/s².

    MCQ No. 131

    A point on the rim of a wheel of radius 0.50 m rotates at 16 rad/s. The linear speed is:

    a. 6 m/s

    b. 7 m/s

    c. 8 m/s

    d. 9 m/s

    Correct Answer: c. 8 m/s

    Explanation:

    v=rω=0.5×16=8 m/sv=r\omega =0.5\times16 =8\text{ m/s}

    MCQ No. 132

    A particle moves in a circle of radius 4 m with speed 12 m/s. The centripetal acceleration is:

    a. 24 m/s²

    b. 30 m/s²

    c. 36 m/s²

    d. 40 m/s²

    Correct Answer: c. 36 m/s²

    Explanation:

    a=v2r=1444=36 m/s2a=\frac{v^2}{r} =\frac{144}{4} =36\text{ m/s}^2

    MCQ No. 133

    A 5 kg object moves at 10 m/s in a circle of radius 20 m. The centripetal force is:

    a. 20 N

    b. 25 N

    c. 30 N

    d. 40 N

    Correct Answer: b. 25 N

    Explanation:

    F=mv2r=5×10020=25 NF=\frac{mv^2}{r} =\frac{5\times100}{20} =25\text{ N}

    MCQ No. 134

    A car rounds a curve of radius 80 m at 20 m/s. The centripetal acceleration is:

    a. 3 m/s²

    b. 4 m/s²

    c. 5 m/s²

    d. 6 m/s²

    Correct Answer: c. 5 m/s²

    Explanation:

    a=40080=5 m/s2a=\frac{400}{80} =5\text{ m/s}^2

    MCQ No. 135

    A car travels around a circular track of radius 100 m at 25 m/s. The required centripetal force per kilogram of mass is:

    a. 4.25 N

    b. 5.25 N

    c. 6.25 N

    d. 7.25 N

    Correct Answer: c. 6.25 N

    Explanation:
    Force per kilogram equals acceleration.

    a=625100=6.25 m/s2a=\frac{625}{100} =6.25\text{ m/s}^2

    MCQ No. 136

    The orbital speed of a satellite is increased. It will move into:

    a. A lower orbit

    b. A higher orbit

    c. The same orbit

    d. A stationary position

    Correct Answer: b. A higher orbit

    Explanation:
    An increase in orbital speed allows the satellite to enter a higher orbit after orbital adjustment.

    MCQ No. 137

    A satellite moves to an orbit having four times the original orbital radius. Its orbital velocity becomes:

    a. Half

    b. Double

    c. Four times

    d. Unchanged

    Correct Answer: a. Half

    Explanation:
    Since

    v∝1rv\propto\frac1{\sqrt r}

    If radius becomes four times,

    v=12v0v=\frac12v_0

    MCQ No. 138

    A torque of 30 N·m acts on a body having moment of inertia 6 kg·m². The angular acceleration is:

    a. 3 rad/s²

    b. 4 rad/s²

    c. 5 rad/s²

    d. 6 rad/s²

    Correct Answer: c. 5 rad/s²

    Explanation:

    α=τI=306=5 rad/s2\alpha=\frac{\tau}{I} =\frac{30}{6} =5\text{ rad/s}^2

    MCQ No. 139

    A flywheel has moment of inertia 8 kg·m² and angular velocity 15 rad/s. Its angular momentum is:

    a. 100 kg·m²/s

    b. 110 kg·m²/s

    c. 120 kg·m²/s

    d. 130 kg·m²/s

    Correct Answer: c. 120 kg·m²/s

    Explanation:

    L=Iω=8×15=120L=I\omega =8\times15 =120

    MCQ No. 140

    A force of 60 N acts at 0.25 m from the axis and makes 90° with the lever arm. The torque is:

    a. 10 N·m

    b. 12 N·m

    c. 15 N·m

    d. 18 N·m

    Correct Answer: c. 15 N·m

    Explanation:

    τ=Fr=60×0.25=15 N.m\tau=Fr =60\times0.25 =15\text{ N·m}

    MCQ No. 141

    A wheel rotates at 600 rpm. Its angular velocity is:

    a. 10π rad/s

    b. 20π rad/s

    c. 30π rad/s

    d. 40π rad/s

    Correct Answer: b. 20π rad/s

    Explanation:
    600 rpm = 10 rev/s

    ω=2π(10)=20π rad/s\omega=2\pi(10)=20\pi\text{ rad/s}

    MCQ No. 142

    A disc rotates at 300 rpm. The angular displacement in 4 s is:

    a. 20π rad

    b. 30π rad

    c. 40π rad

    d. 50π rad

    Correct Answer: c. 40π rad

    Explanation:
    300 rpm = 5 rev/s

    Angular velocity

    =10π rad/s=10\pi\text{ rad/s}
    θ=ωt=10π×4=40π\theta=\omega t =10\pi\times4 =40\pi

    MCQ No. 143

    If the radius of rotation becomes three times while angular velocity remains constant, the linear velocity becomes:

    a. One-third

    b. Same

    c. Double

    d. Three times

    Correct Answer: d. Three times

    Explanation:
    Since

    v=rωv=r\omega

    Linear velocity is directly proportional to radius.

    MCQ No. 144

    A body moving in a circle has speed 18 m/s and centripetal acceleration 27 m/s². The radius of the path is:

    a. 8 m

    b. 10 m

    c. 12 m

    d. 14 m

    Correct Answer: c. 12 m

    Explanation:

    r=v2a=32427=12 mr=\frac{v^2}{a} =\frac{324}{27} =12\text{ m}

    MCQ No. 145

    A cyclist moves around a curve of radius 50 m at 10 m/s. The required centripetal acceleration is:

    a. 1 m/s²

    b. 2 m/s²

    c. 3 m/s²

    d. 4 m/s²

    Correct Answer: b. 2 m/s²

    Explanation:

    a=10050=2 m/s2a=\frac{100}{50} =2\text{ m/s}^2

    MCQ No. 146

    If both the radius and speed of a body are doubled, the centripetal acceleration becomes:

    a. Half

    b. Same

    c. Double

    d. Four times

    Correct Answer: c. Double

    Explanation:

    a=v2ra=\frac{v^2}{r}

    New acceleration

    =(2v)22r=4v22r=2a=\frac{(2v)^2}{2r} =\frac{4v^2}{2r} =2a

    MCQ No. 147

    A rotating wheel completes 15 revolutions in 3 seconds. Its angular velocity is:

    a. 5π5\pi rad/s

    b. 10π10\pi rad/s

    c. 15π15\pi rad/s

    d. 20π20\pi rad/s

    Correct Answer: b. 10π10\pi rad/s

    Explanation:
    Frequency

    f=153=5 Hzf=\frac{15}{3}=5\text{ Hz}
    ω=2πf=10π rad/s\omega=2\pi f=10\pi\text{ rad/s}

    MCQ No. 148

    A rotating body has angular momentum 60 kg·m²/s and moment of inertia 12 kg·m². Its angular velocity is:

    a. 3 rad/s

    b. 4 rad/s

    c. 5 rad/s

    d. 6 rad/s

    Correct Answer: c. 5 rad/s

    Explanation:

    ω=LI=6012=5 rad/s\omega=\frac{L}{I} =\frac{60}{12} =5\text{ rad/s}

    MCQ No. 149

    The escape velocity from Earth is approximately:

    a. 7.9 km/s

    b. 9.8 km/s

    c. 11.2 km/s

    d. 15 km/s

    Correct Answer: c. 11.2 km/s

    Explanation:
    Escape velocity is the minimum speed needed to leave Earth's gravitational field permanently.

    MCQ No. 150

    A body rotates through 12 complete revolutions. The angular displacement is:

    a. 12π12\pi rad

    b. 18π18\pi rad

    c. 20π20\pi rad

    d. 24π24\pi rad

    Correct Answer: d. 24π24\pi rad

    Explanation:
    One revolution equals 2π2\pi radians.

    θ=12×2π=24π rad\theta=12\times2\pi =24\pi\text{ rad}

    MCQ No. 151

    A wheel rotates with an angular velocity of 25 rad/s. If its radius is 0.4 m, the linear velocity of a point on the rim is:

    a. 8 m/s

    b. 10 m/s

    c. 12 m/s

    d. 15 m/s

    Correct Answer: b. 10 m/s

    Explanation:
    Using v=rωv=r\omega ,

    v=0.4×25=10 m/sv=0.4\times25=10\text{ m/s}

    MCQ No. 152

    A body moves in a circle of radius 10 m with a speed of 20 m/s. The centripetal acceleration is:

    a. 20 m/s²

    b. 30 m/s²

    c. 40 m/s²

    d. 50 m/s²

    Correct Answer: c. 40 m/s²

    Explanation:

    ac=v2r=40010=40 m/s2a_c=\frac{v^2}{r} =\frac{400}{10} =40\text{ m/s}^2

    MCQ No. 153

    A 3 kg object moves with a speed of 12 m/s in a circle of radius 6 m. The centripetal force acting on it is:

    a. 48 N

    b. 60 N

    c. 72 N

    d. 84 N

    Correct Answer: c. 72 N

    Explanation:

    F=mv2r=3×1446=72 NF=\frac{mv^2}{r} =\frac{3\times144}{6} =72\text{ N}

    MCQ No. 154

    A wheel accelerates uniformly from 8 rad/s to 32 rad/s in 6 s. Its angular acceleration is:

    a. 2 rad/s²

    b. 3 rad/s²

    c. 4 rad/s²

    d. 5 rad/s²

    Correct Answer: c. 4 rad/s²

    Explanation:

    α=32−86=4 rad/s2\alpha=\frac{32-8}{6}=4\text{ rad/s}^2

    MCQ No. 155

    A disc rotates through 180 rad in 10 s starting from rest. Its angular acceleration is:

    a. 2.6 rad/s²

    b. 3.2 rad/s²

    c. 3.6 rad/s²

    d. 4.0 rad/s²

    Correct Answer: c. 3.6 rad/s²

    Explanation:
    Using

    θ=12αt2\theta=\frac12\alpha t^2
    180=12α(100)180=\frac12\alpha(100)
    α=360100=3.6 rad/s2\alpha=\frac{360}{100}=3.6\text{ rad/s}^2

    MCQ No. 156

    A force of 50 N acts perpendicular to a lever arm of 0.6 m. The torque produced is:

    a. 20 N·m

    b. 25 N·m

    c. 30 N·m

    d. 35 N·m

    Correct Answer: c. 30 N·m

    Explanation:

    τ=Fr=50×0.6=30 N.m\tau=Fr=50\times0.6=30\text{ N·m}

    MCQ No. 157

    A body has a moment of inertia of 4 kg·m². If a torque of 24 N·m acts on it, its angular acceleration will be:

    a. 4 rad/s²

    b. 5 rad/s²

    c. 6 rad/s²

    d. 7 rad/s²

    Correct Answer: c. 6 rad/s²

    Explanation:

    α=τI=244=6 rad/s2\alpha=\frac{\tau}{I} =\frac{24}{4} =6\text{ rad/s}^2

    MCQ No. 158

    A flywheel has a moment of inertia of 10 kg·m² and rotates at 12 rad/s. Its angular momentum is:

    a. 100 kg·m²/s

    b. 110 kg·m²/s

    c. 120 kg·m²/s

    d. 140 kg·m²/s

    Correct Answer: c. 120 kg·m²/s

    Explanation:

    L=Iω=10×12=120 kg\cdotpm2/sL=I\omega =10\times12 =120\text{ kg·m}^2/\text{s}

    MCQ No. 159

    A particle moves in a circle with angular velocity 8 rad/s and radius 3 m. The centripetal acceleration is:

    a. 96 m/s²

    b. 144 m/s²

    c. 192 m/s²

    d. 256 m/s²

    Correct Answer: c. 192 m/s²

    Explanation:

    a=rω2=3×64=192 m/s2a=r\omega^2 =3\times64 =192\text{ m/s}^2

    MCQ No. 160

    A satellite orbits Earth at a height where the orbital radius is doubled. Compared with its original value, its orbital period becomes approximately:

    a. 2 times

    b. 2.8 times

    c. 4 times

    d. 8 times

    Correct Answer: b. 2.8 times

    Explanation:
    According to Kepler's Third Law,

    T∝r3/2T\propto r^{3/2}

    If radius doubles,

    T=23/2T≈2.83TT=2^{3/2}T\approx2.83T

    MCQ No. 161

    A fan rotates at 240 rpm. Its angular velocity is:

    a. 4π4\pi rad/s

    b. 6π6\pi rad/s

    c. 8π8\pi rad/s

    d. 10π10\pirad/s

    Correct Answer: c. 8π8\pi rad/s

    Explanation:
    240 rpm = 4 rev/s

    ω=2π(4)=8π rad/s\omega=2\pi(4)=8\pi\text{ rad/s}

    MCQ No. 162

    A rotating disc completes 150 revolutions in 30 seconds. Its angular velocity is:

    a. 5π5\pi rad/s

    b. 10π10\pi rad/s

    c. 15π15\pi rad/s

    d. 20π20\pi rad/s

    Correct Answer: b. 10π10\pi rad/s

    Explanation:
    Frequency

    f=15030=5 Hzf=\frac{150}{30}=5\text{ Hz}
    ω=2πf=10π\omega=2\pi f=10\pi

    MCQ No. 163

    If the angular velocity of a rotating body is tripled while the radius remains constant, its centripetal acceleration becomes:

    a. Three times

    b. Six times

    c. Nine times

    d. Twelve times

    Correct Answer: c. Nine times

    Explanation:
    Since

    a=rω2a=r\omega^2

    tripling angular velocity increases acceleration by 32=93^2=9.

    MCQ No. 164

    A body moving in a circle has speed 24 m/s and radius 18 m. The centripetal acceleration is:

    a. 24 m/s²

    b. 28 m/s²

    c. 32 m/s²

    d. 36 m/s²

    Correct Answer: c. 32 m/s²

    Explanation:

    a=24218=57618=32 m/s2a=\frac{24^2}{18} =\frac{576}{18} =32\text{ m/s}^2

    MCQ No. 165

    A body rotates through 25 revolutions. Its angular displacement is:

    a. 25π25\pi rad

    b. 40π40\pi  rad

    c. 50π50\pi  rad

    d. 75π75\pi rad

    Correct Answer: c. 50π50\pi  rad

    Explanation:

    25×2π=50π25\times2\pi=50\pi

    MCQ No. 166

    A particle moving in a circle has a radius of 2.5 m and an angular velocity of 12 rad/s. Its linear speed is:

    a. 24 m/s

    b. 28 m/s

    c. 30 m/s

    d. 36 m/s

    Correct Answer: c. 30 m/s

    Explanation:

    v=rω=2.5×12=30 m/sv=r\omega =2.5\times12 =30\text{ m/s}

    MCQ No. 167

    A body of moment of inertia 15 kg·m² rotates at 6 rad/s. Its angular momentum equals:

    a. 60 kg·m²/s

    b. 75 kg·m²/s

    c. 90 kg·m²/s

    d. 120 kg·m²/s

    Correct Answer: c. 90 kg·m²/s

    Explanation:

    L=Iω=15×6=90L=I\omega =15\times6 =90

    MCQ No. 168

    A torque of 72 N·m acts on a body having moment of inertia 9 kg·m². The angular acceleration is:

    a. 6 rad/s²

    b. 7 rad/s²

    c. 8 rad/s²

    d. 9 rad/s²

    Correct Answer: c. 8 rad/s²

    Explanation:

    α=729=8 rad/s2\alpha=\frac{72}{9}=8\text{ rad/s}^2

    MCQ No. 169

    A wheel of radius 0.2 m rotates at 50 rad/s. The speed of a point on the rim is:

    a. 8 m/s

    b. 10 m/s

    c. 12 m/s

    d. 15 m/s

    Correct Answer: b. 10 m/s

    Explanation:

    v=0.2×50=10 m/sv=0.2\times50=10\text{ m/s}

    MCQ No. 170

    A satellite completes one revolution around Earth in 24 hours. It is most likely:

    a. A polar satellite

    b. A geostationary satellite

    c. A low-Earth satellite

    d. A research satellite

    Correct Answer: b. A geostationary satellite

    Explanation:
    A geostationary satellite has an orbital period equal to Earth's rotational period.

    MCQ No. 171

    A rotating wheel turns 600°. Its angular displacement in radians is:

    a. 8π3\frac{8\pi}{3}

    b. 10π3\frac{10\pi}{3}

    c. 12π3\frac{12\pi}{3}

    d. 5π5\pi 

    Correct Answer: b. 10π3\frac{10\pi}{3}

    Explanation:

    600∘=600π180=10π3600^\circ=\frac{600\pi}{180} =\frac{10\pi}{3}

    MCQ No. 172

    A body rotates at 5 revolutions per second. Its angular velocity is:

    a. 5π5\pi rad/s

    b. 8π8\pi rad/s

    c. 10π10\pi rad/s

    d. 12π12\pi rad/s

    Correct Answer: c. 10π10\pi  rad/s

    Explanation:

    ω=2πf=2π(5)=10π\omega=2\pi f =2\pi(5) =10\pi

    MCQ No. 173

    If the speed of a particle is increased by 50%, the centripetal force becomes:

    a. 1.25 times

    b. 1.5 times

    c. 2.0 times

    d. 2.25 times

    Correct Answer: d. 2.25 times

    Explanation:
    Since

    F∝v2F\propto v^2

    New speed = 1.5v1.5v 

    F=(1.5)2F=2.25FF=(1.5)^2F=2.25F

    MCQ No. 174

    The SI unit of angular acceleration is:

    a. rad

    b. rad/s

    c. rad/s²

    d. rev/s

    Correct Answer: c. rad/s²

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

    MCQ No. 175

    A rotating machine part completes 720 revolutions in 2 minutes. Its rotational speed is:

    a. 240 rpm

    b. 300 rpm

    c. 360 rpm

    d. 480 rpm

    Correct Answer: c. 360 rpm

    Explanation:

    rpm=7202=360 rpm\text{rpm}=\frac{720}{2}=360\text{ rpm}

    MCQ No. 176

    A wheel rotates from rest with a constant angular acceleration of 5 rad/s². The angular displacement after 4 s is:

    a. 20 rad

    b. 30 rad

    c. 40 rad

    d. 50 rad

    Correct Answer: c. 40 rad

    Explanation:
    Using

    θ=12αt2\theta=\frac{1}{2}\alpha t^2
    =12(5)(42)=40 rad=\frac{1}{2}(5)(4^2)=40\text{ rad}

    MCQ No. 177

    A rotating wheel has an initial angular velocity of 12 rad/s and an angular acceleration of 3 rad/s². Find its angular velocity after 8 s.

    a. 30 rad/s

    b. 32 rad/s

    c. 36 rad/s

    d. 40 rad/s

    Correct Answer: c. 36 rad/s

    Explanation:

    ω=ω0+αt\omega=\omega_0+\alpha t
    =12+3(8)=36 rad/s=12+3(8)=36\text{ rad/s}

    MCQ No. 178

    A body rotates through 150 rad while its angular velocity increases from 10 rad/s to 20 rad/s. Its angular acceleration is:

    a. 0.5 rad/s²

    b. 1.0 rad/s²

    c. 1.5 rad/s²

    d. 2.0 rad/s²

    Correct Answer: b. 1.0 rad/s²

    Explanation:
    Using

    ω2=ω02+2αθ\omega^2=\omega_0^2+2\alpha\theta
    202=102+2α(150)20^2=10^2+2\alpha(150)
    400=100+300α400=100+300\alpha
    α=1 rad/s2\alpha=1\text{ rad/s}^2

    MCQ No. 179

    A disc of radius 0.6 m rotates at 30 rad/s. The linear velocity at its edge is:

    a. 12 m/s

    b. 15 m/s

    c. 18 m/s

    d. 20 m/s

    Correct Answer: c. 18 m/s

    Explanation:

    v=rω=0.6×30=18 m/sv=r\omega =0.6\times30 =18\text{ m/s}

    MCQ No. 180

    A particle moves in a circle of radius 5 m with an angular velocity of 6 rad/s. The centripetal acceleration is:

    a. 120 m/s²

    b. 150 m/s²

    c. 180 m/s²

    d. 200 m/s²

    Correct Answer: c. 180 m/s²

    Explanation:

    ac=rω2=5×36=180 m/s2a_c=r\omega^2 =5\times36 =180\text{ m/s}^2

    MCQ No. 181

    A 4 kg object moves in a circle of radius 8 m with a speed of 16 m/s. The centripetal force acting on it is:

    a. 96 N

    b. 112 N

    c. 128 N

    d. 144 N

    Correct Answer: c. 128 N

    Explanation:

    F=mv2r=4×2568=128 NF=\frac{mv^2}{r} =\frac{4\times256}{8} =128\text{ N}

    MCQ No. 182

    A wheel rotates at 180 rpm. Its angular velocity is:

    a. 4π4\pi rad/s

    b. 5π5\pi  rad/s

    c. 6π6\pi rad/s

    d. 8π8\pi rad/s

    Correct Answer: c. 6π6\pi  rad/s

    Explanation:
    180 rpm = 3 rev/s

    ω=2π(3)=6π rad/s\omega=2\pi(3)=6\pi\text{ rad/s}

    MCQ No. 183

    A rotating body completes 20 revolutions in 4 s. Its angular velocity is:

    a. 8π8\pi rad/s

    b. 10π10\pi rad/s

    c. 12π12\pi rad/s

    d. 16π16\pi rad/s

    Correct Answer: b. 10π10\pi rad/s

    Explanation:
    Frequency

    f=204=5 Hzf=\frac{20}{4}=5\text{ Hz}
    ω=2πf=10π\omega=2\pi f =10\pi

    MCQ No. 184

    A force of 80 N acts at a perpendicular distance of 0.25 m from the axis of rotation. The torque produced is:

    a. 10 N·m

    b. 15 N·m

    c. 20 N·m

    d. 25 N·m

    Correct Answer: c. 20 N·m

    Explanation:

    τ=Fr=80×0.25=20 N.m\tau=Fr =80\times0.25 =20\text{ N·m}

    MCQ No. 185

    A body has a moment of inertia of 12 kg·m². If a torque of 48 N·m acts on it, the angular acceleration will be:

    a. 2 rad/s²

    b. 3 rad/s²

    c. 4 rad/s²

    d. 5 rad/s²

    Correct Answer: c. 4 rad/s²

    Explanation:

    α=τI=4812=4 rad/s2\alpha=\frac{\tau}{I} =\frac{48}{12} =4\text{ rad/s}^2

    MCQ No. 186

    A flywheel has an angular momentum of 200 kg·m²/s and a moment of inertia of 20 kg·m². Its angular velocity is:

    a. 8 rad/s

    b. 9 rad/s

    c. 10 rad/s

    d. 12 rad/s

    Correct Answer: c. 10 rad/s

    Explanation:

    ω=LI=20020=10 rad/s\omega=\frac{L}{I} =\frac{200}{20} =10\text{ rad/s}

    MCQ No. 187

    If the radius of a circular path is reduced to one-half while the speed remains constant, the centripetal acceleration becomes:

    a. Half

    b. Same

    c. Double

    d. Four times

    Correct Answer: c. Double

    Explanation:
    Since

    a=v2ra=\frac{v^2}{r}

    halving the radius doubles the centripetal acceleration.

    MCQ No. 188

    A satellite moves from a lower orbit to a higher orbit. Its orbital period will:

    a. Decrease

    b. Remain constant

    c. Increase

    d. Become zero

    Correct Answer: c. Increase

    Explanation:
    According to Kepler's Third Law, satellites in higher orbits have longer orbital periods.

    MCQ No. 189

    The escape velocity of Earth is approximately:

    a. 7.9 km/s

    b. 9.8 km/s

    c. 11.2 km/s

    d. 13.5 km/s

    Correct Answer: c. 11.2 km/s

    Explanation:
    Escape velocity is the minimum speed required for an object to leave Earth's gravitational field permanently.

    MCQ No. 190

    A wheel rotates through 900°. Its angular displacement in radians is:

    a. 3π3\pi 

    b. 4π 

    c. 5π 

    d. 6π6\pi 

    Correct Answer: c. 5π5\pi 

    Explanation:

    900∘=900π180=5π rad900^\circ =\frac{900\pi}{180} =5\pi\text{ rad}

    MCQ No. 191

    A point on the rim of a wheel has a linear speed of 18 m/s. If the wheel radius is 0.9 m, its angular velocity is:

    a. 18 rad/s

    b. 20 rad/s

    c. 22 rad/s

    d. 24 rad/s

    Correct Answer: b. 20 rad/s

    Explanation:

    ω=vr=180.9=20 rad/s\omega=\frac{v}{r} =\frac{18}{0.9} =20\text{ rad/s}

    MCQ No. 192

    A rotating machine completes 1500 revolutions in 5 minutes. Its rotational speed is:

    a. 250 rpm

    b. 300 rpm

    c. 350 rpm

    d. 400 rpm

    Correct Answer: b. 300 rpm

    Explanation:

    rpm=15005=300\text{rpm} =\frac{1500}{5} =300

    MCQ No. 193

    A cyclist takes a turn of radius 25 m at 15 m/s. The required centripetal acceleration is:

    a. 7 m/s²

    b. 8 m/s²

    c. 9 m/s²

    d. 10 m/s²

    Correct Answer: c. 9 m/s²

    Explanation:

    a=15225=22525=9 m/s2a=\frac{15^2}{25} =\frac{225}{25} =9\text{ m/s}^2

    MCQ No. 194

    A particle moving in a circle has a centripetal acceleration of 16 m/s² and radius 4 m. Its speed is:

    a. 6 m/s

    b. 8 m/s

    c. 10 m/s

    d. 12 m/s

    Correct Answer: b. 8 m/s

    Explanation:

    v=ar=16×4=64=8 m/sv=\sqrt{ar} =\sqrt{16\times4} =\sqrt{64} =8\text{ m/s}

    MCQ No. 195

    The moment of inertia of a body is doubled while its angular velocity is halved. The angular momentum becomes:

    a. One-half

    b. Same

    c. Double

    d. Four times

    Correct Answer: b. Same

    Explanation:

    L=IωL=I\omega

    New angular momentum:

    (2I)(ω2)=Iω(2I)\left(\frac{\omega}{2}\right)=I\omega

    Hence, it remains unchanged.

    MCQ No. 196

    A rotating disc has an angular velocity of 40 rad/s. After applying brakes, it stops uniformly in 8 s. The angular deceleration is:

    a. 3 rad/s²

    b. 4 rad/s²

    c. 5 rad/s²

    d. 6 rad/s²

    Correct Answer: c. 5 rad/s²

    Explanation:

    α=0−408=−5 rad/s2\alpha=\frac{0-40}{8} =-5\text{ rad/s}^2

    Magnitude = 5 rad/s².

    MCQ No. 197

    A body rotates through 50 revolutions. The angular displacement is:

    a. 50π50\pi  rad

    b. 75π75\pi  rad

    c. 100π100\pi  rad

    d. 120π120\pi  rad

    Correct Answer: c. 100π100\pi  rad

    Explanation:
    One revolution equals 2π2\pi  radians.

    50×2π=100π50\times2\pi =100\pi

    MCQ No. 198

    A body has an angular momentum of 72 kg·m²/s and rotates with angular velocity 9 rad/s. Its moment of inertia is:

    a. 6 kg·m²

    b. 7 kg·m²

    c. 8 kg·m²

    d. 9 kg·m²

    Correct Answer: c. 8 kg·m²

    Explanation:

    I=Lω=729=8 kg.m2I=\frac{L}{\omega} =\frac{72}{9} =8\text{ kg·m}^2

    MCQ No. 199

    A rotating wheel has an angular velocity of 24 rad/s and radius 0.75 m. The tangential speed of a point on its rim is:

    a. 16 m/s

    b. 18 m/s

    c. 20 m/s

    d. 22 m/s

    Correct Answer: b. 18 m/s

    Explanation:

    v=rω=0.75×24=18 m/sv=r\omega =0.75\times24 =18\text{ m/s}

    MCQ No. 200

    A figure skater reduces her moment of inertia to one-third of its original value while no external torque acts. Her angular velocity becomes:

    a. One-third of the original

    b. One-half of the original

    c. Three times the original

    d. Nine times the original

    Correct Answer: c. Three times the original

    Explanation:
    Using the law of conservation of angular momentum,

    I1ω1=I2ω2I_1\omega_1=I_2\omega_2

    If

    I2=I13,I_2=\frac{I_1}{3},

    then

    ω2=3ω1.\omega_2=3\omega_1.

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