1. Tardigrade
  2. Question
  3. Physics
  4. A solid cylinder and a solid sphere, having same mass M and radius R, roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be :

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. A solid cylinder and a solid sphere, having same mass $M$ and radius $R$, roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be :

JEE MainJEE Main 2022System of Particles and Rotational Motion

Solution:

$ V =\sqrt{\frac{2 gH }{1+ k ^2 / R ^2}}$
$ \frac{ V _{\text {cylinder }}}{ V _{\text {sphere }}}=\sqrt{\frac{\left(1+ k ^2 / R ^2\right)_{\text {sphere }}}{\left(1+ k ^2 / R ^2\right)_{\text {cylinder }}}} $
$ =\sqrt{\frac{1+2 / 5}{1+1 / 2}}=\sqrt{\frac{7}{5} \times \frac{2}{3}}=\sqrt{\frac{14}{15}}$