Uniform Circular Motion – Advanced Single-Concept Numerical Problems

 

JEE Advanced Physics Worksheet

Uniform Circular Motion – Advanced Single-Concept Numerical Problems

20 High-Difficulty MCQs (2–4 Step Calculations)

Level: JEE Advanced • Olympiad Foundation • Advanced NEET

Take $g=10~\text{m/s}^2$ unless stated otherwise.

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1. Relative Motion on a Rotating Disc

A horizontal disc of radius $0.8\,\text{m}$ rotates at $2\,\text{rad s}^{-1}$. An ant starts walking radially outward from the centre with constant speed $0.4\,\text{m s}^{-1}$ relative to the disc. When it reaches the rim, its acceleration with respect to the ground is

A) $3.20$

B) $3.35$

C) $3.52$

D) $4.00$

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2. Banked Road with Friction

A road is banked at $30^\circ$. Radius of curvature is $50\,\text{m}$. Coefficient of friction between tyre and road is $0.20$. The maximum speed without skidding upward is

A) 24 m/s

B) 28 m/s

C) 31 m/s

D) 35 m/s

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3. Vertical Circle

A particle tied to a light string moves in a vertical circle of radius $2\,\text{m}$. If tension at the highest point is $2mg$, the speed at the lowest point is

A) $\sqrt{70}$

B) $8\sqrt2$

C) 10

D) $6\sqrt3$

m/s

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4. Conical Pendulum

A bob of mass $0.5\,\text{kg}$ revolves in a horizontal circle making an angle $60^\circ$ with the vertical. If string length is $2\,\text{m}$, the angular speed is

A) $\sqrt5$

B) $\sqrt{10}$

C) $\sqrt{\mathrm{15}}$

D) $2\sqrt5$

rad/s

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5. Rotating Platform

A block is placed $0.5\,\text{m}$ from the centre of a rotating platform. Coefficient of friction is 0.40. Maximum angular velocity before slipping is

A) 2 rad/s

B) $2\sqrt5$ rad/s

C) $4\sqrt2$ rad/s

D) $4\sqrt5$ rad/s

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6. Relative Motion

Two particles move on the same circle of radius $5\,\text{m}$ with speeds $8$ and $6\,\text{m/s}$ in opposite directions. Magnitude of relative acceleration is

A) 20

B) 25.6

C) 32

D) 40

m/s²

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7. Ferris Wheel

Radius = 12 m. Period = 8 s. The apparent weight of a 60 kg person at the top is

A) 225 N

B) 245 N

C) 305 N

D) 365 N

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8. Variable Radius

A particle moves with constant speed 20 m/s. Radius changes from 8 m to 2 m. Ratio of centripetal accelerations is

A) 2

B) 4

C) 8

D) 16

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9. Satellite

An artificial satellite moves in a circular orbit where gravitational acceleration is 5 m/s².

Orbital speed is

A) 4 km/s

B) 5 km/s

C) 6 km/s

D) Depends on orbital radius

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10. Maximum Tension

A string withstands maximum tension 180 N.

A 2 kg mass rotates in horizontal circle of radius 1.8 m.

Maximum speed is

A) 9

B) 10

C) $9\sqrt2$

D) $3\sqrt{15}$

m/s

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11. Motorcycle on Banked Curve

Radius =100 m    Bank angle =37°    No friction.   Correct speed is

A) 20

B) 25

C) 27.3

D) 30

m/s

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12. Pulley + Circular Motion

A particle moves in a horizontal circle of radius 1 m. String passes through smooth hole and supports another mass. If hanging mass =2 kg and rotating mass =1 kg,

Speed required is

A) $\sqrt{10}$

B) $2\sqrt5$

C) $2\sqrt{10}$

D) $4\sqrt{\mathrm{5}}$

m/s

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13. Bead on Rotating Wire

A bead rests on a smooth rotating horizontal wire. Distance from axis =0.4 m  Angular speed =5 rad/s   Normal reaction is

A) 5 m

B) 8 m

C) 10 m

D) 12 m

N

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14. Coin on Turntable

Radius =0.25 m Coefficient of friction =0.60 Maximum rpm before slipping

A) 42

B) 47

C) 52

D) 60

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15. Aircraft Turn

Aircraft speed =250 m/s Radius =5 km Bank angle is closest to

A) 42°

B) 48°

C) 52°

D) 58°

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16. Vertical Circle

Minimum speed at bottom to complete circle Radius=5 m

A) 10

B) $5\sqrt5$

C) $10\sqrt2$

D) $5\sqrt6$

m/s

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17. Relative Motion

Two particles start from same point moving clockwise and anticlockwise. Radius=4 m Speeds=8 and 12 m/s. Relative acceleration immediately after start is

A) 20

B) 40

C) 50

D) 52

m/s²

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18. Conical Pendulum

Length=1.25 m Angular speed=4 rad/s Angle with vertical is

A)30°

B)45°

C)60°

D)75°

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19. Rotating Ring

A small bead rotates inside a smooth vertical ring. Radius=0.5 m. Minimum speed at top to maintain contact

A) $\sqrt5$

B) $\sqrt{10}$

C) $2\sqrt5$

D) 5

m/s

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20. Combined Energy + Circular Motion

A particle slides from rest through a vertical height of 20 m into a smooth loop of radius 5 m. Speed at highest point is

A)10

B)$10\sqrt2$

C)$10\sqrt3$

D)20

m/s

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Answer Key

Q	Ans
1	C
2	C
3	B
4	B
5	B
6	C
7	B
8	B
9	D
10	C
11	C
12	B
13	C
14	B
15	C
16	B
17	D
18	C
19	A
20	C