Question

A body rolls down an inclined plane. If its K.E. of rotational motion is $\text{40\%}$ of its K.E. of translational , then the body is a

• A. Cylinder
• B. Ring
• C. Solid Disc
• D. Solid sphere

Answer 1

The correct option is D Solid sphere

$K{E}_{rotational}=40$% of $K{E}_{translational}$

$⟹\frac{1}{2}I{w}^2=0.4\times \frac{1}{2}m{v}^2⟹\frac{1}{2}I{\omega }^2=0.4\times \frac{1}{2}m{r}^2{\omega }^2$ as $v=r\omega$

$⟹I=0.4m{r}^2$

As we know $I=m{K}^2⟹0.4m{r}^2=m{K}^2$

$K=\sqrt{\frac{2}{5}}r$

Thus its a solid sphere.