Question

A mass $m$ of radius $r$ is rolling horizontally without any slip with a linear speed $v$. It then rolls up to a height given by $\frac{3}{4}\frac{y^2}{g}$

• A. the body is identified to be a disc or a solid cylinder
• B. the body is a solid sphere
• C. moment of inertia of the body about instantaneous axis of rotation is $\frac{3}{2}m{r}^2$
• D. moment of inertia of the body about instantaneous axis of rotation is $\frac{7}{5}m{r}^2$

Answer 1

Answer: (A), (C)

The correct options are
A the body is identified to be a disc or a solid cylinder
C moment of inertia of the body about instantaneous axis of rotation is $\frac{3}{2}m{r}^2$

$\frac{K_R}{k_r}=\frac{I}{m{r}^2}$
$\therefore k_r=\left(\frac{m{r}^2}{I+m{r}^2}\right)k_{Total}$
or $k_{Total}=\left(\frac{I+m{r}^2}{m{r}^2}\right)\left(\frac{1}{2}m{v}^2\right)$
$=mgh=mg\left(\frac{3}{4}\frac{v^2}{g}\right)$
Solving we get $I=\frac{1}{2}m{r}^2$ So it is either solid cylinder or disc.