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 $\frac{3v^2}{4g}$. Which of the following is/are correct?

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

Answer 1

Answer: (A), (C)

MOl of the body about instantaneous axis of rotation is $\frac{3}{2}m{r}^2$

Use $v=\sqrt{\frac{2gh}{\beta }}$
where, $\beta =1+\frac{I}{M{r}^2}$
$v^2.\beta =\left[2g\left(3v^2/4g\right)\right]\Rightarrow \beta =3/2$
$\Rightarrow$ $I=\left[\right(\beta -1\left)m{r}^2\right]=1/2m{r}^2$

So body is a disc or solid cylinder

MOI about instantaneous axis of rotation $=1/2m{r}^2+m{r}^2=3/2m{r}^2$