MCQ
For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is $\frac{x}{5}$. The value of $x$ is ................
- A$4$
- B$6$
- C$8$
- ✓$2$
✓
Answer
Correct option: D.
$2$
d
$\frac{ K _{\text {rot }}}{ K _{\text {Total }}}=\frac{\frac{1}{2}\left(\frac{2}{3} mR ^2\right)\left(\frac{ V }{ R }\right)^2}{\frac{1}{2} mv ^2+\frac{1}{2}\left(\frac{2}{3} mR ^2\right)\left(\frac{ V }{ R }\right)^2}$
$\frac{ K _{\text {rot }}}{ K _{\text {Total }}}=\frac{\frac{1}{2}\left(\frac{2}{3} mR ^2\right)\left(\frac{ V }{ R }\right)^2}{\frac{1}{2} mv ^2+\frac{1}{2}\left(\frac{2}{3} mR ^2\right)\left(\frac{ V }{ R }\right)^2}$
$\Rightarrow \frac{ x }{5}=\frac{2}{5} \Rightarrow x =2$
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