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A sphere of mass m and radius R is kept ...

A sphere of mass m and radius R is kept on a rough floor. A sharp impulse is applied in the horizontal direction at the height of centre of sphere so that sphere acquires a linear velocity `v_(0)` without any angular velocity. Calculate the velocity of sphere when pure rolling starts.

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To solve the problem, we need to analyze the motion of the sphere after the impulse is applied. The sphere starts with a linear velocity \( v_0 \) and no angular velocity. We will find the velocity of the sphere when pure rolling starts. ### Step-by-Step Solution: 1. **Understanding the Initial Conditions**: - The sphere has a mass \( m \) and radius \( R \). - It is given a sharp impulse that imparts a linear velocity \( v_0 \) without any initial angular velocity. ...
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