Question 120: Centre of Mass and Rotational Motion

Question

A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be $t_1$ and $t_2$, respectively, then

Accepted Answer

$$\begin{aligned}
& \mathrm{t}=\sqrt{\frac{2 \ell}{\mathrm{a}_{\mathrm{cm}}}} \
& \mathrm{a}_{\mathrm{cm}}=\frac{\mathrm{g} \sin 	heta}{1+\frac{\mathrm{I}_{\mathrm{cm}}}{\mathrm{MR}^2}} \
& \mathrm{a}_1=\mathrm{a}_{\mathrm{cm}_1}=\frac{5 \mathrm{~g} \sin 	heta}{7} \ldots . . 	ext { Solid } \
& \mathrm{a}_2=\mathrm{a}_{\mathrm{cm}_2}=\frac{3 \mathrm{~g} \sin 	heta}{5} \ldots . 	ext { Hollow } \
& \mathrm{a}_1>\mathrm{a}_2 \
& \mathrm{t}_1<\mathrm{t}_2
\end{aligned}$$

Answer

$t_1< t_2$

Answer

$t_1=2 t_2$

Answer

$t_1 >t_2$

Answer

$t_1=t_2$

Centre of Mass and Rotational Motion

A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be t_1 and t_2, respectively, then

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