Practicing Success

Target Exam

CUET

Subject

Physics

Chapter

System of Particle and Rotational Motion

Question:

A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination. In each case, the ball will : 

Options:

Reach the bottom at the same time and keeps rolling

Will take longer time to roll down one plane

Reach the bottom at the same time

Reach the bottom at an unpredictable time

Correct Answer:

Will take longer time to roll down one plane

Explanation:

Acceleration of the rolling sphere : 

a = gsinθ/((1+k2/R2))

Velocity of the sphere at the bottom of the inclined plane :

v=√(2gh/((1+k2/R2)))

The sphere will take a longer time to roll down one plane than the other. It will take a larger time in case if the plane with smaller inclination because the acceleration is proportional to sin θ.