JEE Main · PhysicsHard
A uniform solid sphere of mass $M$ and radius $R$ is projected with a velocity $v_0$ and an angular velocity $\omega_0$ on a rough horizontal surface. The coefficient of kinetic friction is $\mu$. The time after which the sphere begins pure rolling is given by:
- A.$t = \frac{2v_0 - R\omega_0}{7\mu g}$
- B.$t = \frac{2v_0 + R\omega_0}{7\mu g}$
- C.$t = \frac{v_0 - R\omega_0}{\mu g}$
- D.$t = \frac{2v_0 + R\omega_0}{2\mu g}$
Show correct answer & step-by-step solution
Correct answer: B — $t = \frac{2v_0 + R\omega_0}{7\mu g}$
Solution
Pure rolling occurs when . Using the equations of motion and where , we solve for when .
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