Question

A sphere is released from rest at the top of an inclined plane. What is the speed of the sphere at a distance 6.0 m below its starting point. Assume that the sphere rolls without slipping.

Answer 1

Initial Kinetic Energy will be 0 since it was started from rest. Let mass of sphere be "m" and of radius "r", its final speed be "v" anf let it be initially at a height "h" from the ground.

Then Using Conservation of Energy

Initial Total Energy= Final Total Energy

  

(Since it rolls without slipping thus will have rotational kinetic energy also denoted above as R.K.E)

using the known formulas for energy,

  ............................(1)

where I= Moment of inertia of solid sphere, I= 2mr²/5

and = angular velocity of sphere

then using above values in equation 1, we get

  

  

  

  (ANS)