Question

cylinder is released from rest from the top of an incline of inclination $\theta$ and length ${}^{\prime }{l}^{\prime }$. If the cylinder roles without slipping its speed at the bottom.

• A. $\sqrt{\frac{4gl\sin \theta }{3}}$
• B. $\sqrt{\frac{3gl\sin \theta }{2}}$
• C. $\sqrt{\frac{4gl}{3\sin \theta }}$
• D. $\sqrt{\frac{3g\sin \theta }{3l}}$

Answer 1

The correct option is A $\sqrt{\frac{4gl\sin \theta }{3}}$

Gain is KE= loss in PE

$\frac{1}{2}I{w}^2+\frac{1}{2}m{v}^2=mg\ell \sin \theta$

$\frac{1}{2}\left[\frac{1}{2}m{R}^2\right]w^2+\frac{1}{2}m{v}^2-\frac{3}{4}m{v}^2=mg\ell \sin \theta$

$v=\sqrt{\frac{4g\ell \sin \theta }{3}}$