# A solid sphere is rolling purely on a rough horizontal surface (coefficient of kinetic friction = #mu#) with speed of center #= u#. It collides inelastically with a smooth vertical wall at a certain moment. The coefficient of restitution being #1/2#?

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The time when the sphere will start pure rolling is?

Proceed with your approach. But I have a question, can this problem be solved using linear impulse-momentum theorem and/or angular impulse-momentum theorem?

The time when the sphere will start pure rolling is?

Proceed with your approach. But I have a question, can this problem be solved using linear impulse-momentum theorem and/or angular impulse-momentum theorem?

##### 1 Answer

#### Explanation:

Well,while taking an attempt to solve this,we can say that initially pure rolling was occurring just because of

But as the collision took place,its linear velocity decreases but during collision there was no change inhence

Now,given,coefficient of restitution is

So,new angular velocity becomes

Now,external torque acting due to frictional force,

So,

so,

And,considering linear force,we get,

so,

Now,let after time

and,after time

For pure rolling motion,

Putting the values of