Circular dynamics on level and banked roads — NEET & JEE Questions

Question 1 · difficulty L1 · recall

For uniform circular motion, the centripetal acceleration is directed

• A. toward the centre of the circle
• B. tangentially forward
• C. radially outward
• D. opposite to velocity only

Question 2 · difficulty L2 · understanding

The magnitude of centripetal force required for a body of mass m moving at speed v in a circle of radius r is

• A. $\frac{mv^2}{r}$
• B. $mvr$
• C. $\frac{mr}{v^2}$
• D. $\frac{mv}{r^2}$

Question 3 · difficulty L2 · understanding

On a level circular road, the centripetal force for a turning car is supplied mainly by

• A. friction between tyres and road
• B. the car's weight alone
• C. the normal reaction alone
• D. engine power directly

Question 4 · difficulty L2 · understanding

The purpose of banking a road is to

• A. allow a component of normal reaction to help provide centripetal force
• B. remove gravity
• C. make friction always zero at every speed
• D. increase vehicle mass

Question 5 · difficulty L3 · understanding

A particle moving with uniform speed in a circular path maintains:

• A. Constant velocity
• B. Constant acceleration
• C. Constant velocity but varying acceleration
• D. Varying velocity and varying acceleration

Question 6 · difficulty L3 · application

A 1000 kg car moves at 10 m/s around a level curve of radius 50 m. What centripetal force is required?

• A. 2000 N
• B. 5000 N
• C. 10000 N
• D. 200 N

Question 7 · difficulty L3 · application

If a car's speed on the same circular path doubles, the required centripetal force becomes

• A. four times
• B. twice
• C. half
• D. unchanged

Question 8 · difficulty L3 · application

On a frictionless banked road of angle $\theta$ and radius r, the design speed satisfies

• A. $\tan\theta=\frac{v^2}{rg}$
• B. $\tan\theta=\frac{rg}{v^2}$
• C. $\sin\theta=\frac{v}{rg}$
• D. $v=rg\tan\theta$

Question 9 · difficulty L4 · application

A frictionless banked curve has radius 40 m and angle such that $\tan\theta=0.25$. Taking g = 10 m/s², what is the design speed?

• A. 10 m/s
• B. 20 m/s
• C. 5 m/s
• D. 40 m/s

Question 10 · difficulty L4 · application

A car moves on a level circular road of radius 20 m where the coefficient of static friction is 0.5. Taking g = 10 m/s², the maximum speed without skidding is

• A. 10 m/s
• B. 5 m/s
• C. 20 m/s
• D. 14.1 m/s