# Rotational Dynamics IIT JEE Test

1. A uniform ball, of mass m = 10.00 kg and radius r = 6 cm, rolls smoothly from rest down a ramp at angle 30°. The ball descends a vertical height h =1.20 m to reach the bottom of the ramp. What is its speed at the bottom?

2. A uniform ball, of mass m = 10.00 kg and radius r = 10 cm, rolls smoothly from rest down a ramp at angle 30°. What is the magnitude of the frictional force on the ball as it rolls down the ramp?

3. A thin spherical shell, of mass m = 10.00 kg and radius r = 8 cm, rolls smoothly from rest down a ramp at angle 30°. The ball descends a vertical height h =1.20 m to reach the bottom of the ramp. What is its speed at the bottom?

4. A thin spherical shell, of mass m = 10.00 kg and radius r = 15 cm, rolls smoothly from rest down a ramp at angle 30°. What is the magnitude of the frictional force on the ball as it rolls down the ramp?

5. A uniform ball, of mass m = 10 kg and radius r = 1 cm, slides smoothly from rest down a ramp at angle 45°. A particle is projected from the top of the ramp at an angle 45°, with an initial velocity of u m/s in the direction of slope .The ball descends a vertical height h =50 m to reach the bottom of the ramp. If particle hits the ball after 2 sqrt(2) seconds then what is the value of u?

6. A uniform ball, of mass m = 10 kg and radius r = 1 cm, slides smoothly from rest down a ramp at angle 45°. A particle is projected from the top of the ramp at an angle 45°, with an initial velocity of 4.9 m/s in the direction of slope .The ball descends a vertical height h =50 m to reach the bottom of the ramp. If particle hits the ball after t s seconds then what is the value of t?

7. A uniform ball, of mass m = 10 kg and radius r = 1 cm, slides smoothly from rest down a ramp at angle 45°. A particle is projected from the top of the ramp at an angle 45°, with an initial velocity of u m/s in the direction of slope .The ball descends a vertical height h =50 m to reach the bottom of the ramp. If particle hits the ball after sqrt(2) s then what is the magnitude of relative velocity of the particle with respect to the ball? (approximately)

8. A uniform ball, of mass m = 5 kg and radius r = 2 cm, rolls smoothly from rest down a ramp at angle 44° 26’. A particle is projected from the top of the ramp at an angle 44° 26’, with an initial velocity of u m/s in the direction of slope .The ball descends a vertical height h =50 m to reach the bottom of the ramp. If particle hits the ball after 3.346 s seconds then what is the value of u?

9. A uniform ball, of mass m = 5 kg and radius r = 1 cm, rolls smoothly from rest down a ramp at angle 44° 26’. A particle is projected from the top of the ramp at an angle 44° 26’, with an initial velocity of 4.9 m/s in the direction of slope .The ball descends a vertical height h =50 m to reach the bottom of the ramp. If particle hits the ball after t s seconds then what is the value of t?

10. A uniform ball, of mass m = 15 kg and radius r = 1.0 cm, rolls smoothly from rest down a ramp at angle 44° 26’. A particle is projected from the top of the ramp at an angle 44° 26’, with an initial velocity of 4.9 m/s in the direction of slope .The ball descends a vertical height h =50 m to reach the bottom of the ramp. If particle hits the ball after sqrt(2)s then what is the magnitude of relative velocity of the particle with respect to the ball? (approximately)

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