Question

From a uniform wire, two circular loops are made. One loop $P$ of radius $r$ and the other $Q$ of radius $nr$. If the moment of inertia of $Q$ about an axis passing through its centre and perpendicular to its plane is $8$ times that of $P$ about a similar axis, the value of $n$ is (diameter of the wire is very much smaller than $r$ or $nr$):

• A. $8$
• B. $6$
• C. $4$
• D. $2$

Answer 1

The correct option is D $2$

$I_P=m{r}^2$
$I_Q=nm(nr{)}^2=n^{3}m{r}^2$
Now

$8I_P=I_Q$ ( as given in question)
$n^{3}m{r}^2=8m{r}^2$

$n=2$