Question 430: Centre of Mass and Rotational Motion

Question

A solid sphere of mass $$1 \mathrm{~kg}$$ rolls without slipping on a plane surface. Its kinetic energy is $$7 	imes 10^{-3} \mathrm{~J}$$. The speed of the centre of mass of the sphere is __________ $$\operatorname{cm~s}^{-1}$$

Accepted Answer

$\frac{1}{2} \mathrm{mv}^{2}+\frac{1}{2} \mathrm{I} \omega^{2}=7 	imes 10^{-3}$
$$ \Rightarrow $$ $\frac{1}{2} \mathrm{mv}^{2}+\frac{1}{2}\left(\frac{2}{5} \mathrm{MR}^{2}ight)\left(\frac{\mathrm{V}}{\mathrm{R}}ight)^{2}=7 	imes 10^{-3}$
$$ \Rightarrow $$ $\frac{1}{2} \mathrm{MV}^{2}\left[1+\frac{2}{5}ight]=7 	imes 10^{-3}$
$$ \Rightarrow $$ $\frac{1}{2}(1)\left(\mathrm{V}^{2}ight)\left(\frac{7}{5}ight)=7 	imes 10^{-3}$
$$ \Rightarrow $$ $\mathrm{V}^{2}=10^{-2}$
$$ \Rightarrow $$ $\mathrm{V}=10^{-1}=0.1 \mathrm{~m} / \mathrm{s}=10 \mathrm{~cm} / \mathrm{s}$

Centre of Mass and Rotational Motion

A solid sphere of mass $1 \mathrm{~kg} rolls without slipping on a plane surface. Its kinetic energy is 7 \times 10^{-3} \mathrm{~J}. The speed of the centre of mass of the sphere is __________ \operatorname{cm~s}^{-1}

Choose the correct answer: