Question 152: Centre of Mass and Rotational Motion

Question

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 :

Accepted Answer

$$a = {{g\sin 	heta } \over {1 + {{{K^2}} \over {{R^2}}}}}$$
$$v = \sqrt {{{2Sg\sin 	heta } \over {1 + {{{K^2}} \over {{R^2}}}}}} $$
$$ \Rightarrow {{{v_c}} \over {{v_{ss}}}}\sqrt {{{1 + {{K_{ss}^2} \over {{R^2}}}} \over {1 + {{K_c^2} \over {{R^2}}}}}}  = \sqrt {{{1 + {2 \over 5}} \over {1 + {1 \over 2}}}} $$
$$ \Rightarrow \sqrt {{{{7 \over 5}} \over {{3 \over 2}}}}  = \sqrt {{{14} \over {15}}} $$

Answer

$$\sqrt{\frac{5}{3}}$$

Answer

$$\sqrt{\frac{4}{5}}$$

Answer

$$\sqrt{\frac{3}{5}}$$

Answer

$$\sqrt{\frac{14}{15}}$$

Centre of Mass and Rotational Motion

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 :

Choose the correct answer: