Question

Calculate the M.I. of a thin uniform ring about an axis tangent to the ring and in a plane of the ring, if its M.I. about an axis passing through the centre and perpendicular to plane is $4kg{m}^2.$

• A. $12kg{m}^2$
• B. $3kg{m}^2$
• C. $6kg{m}^2$
• D. $9kg{m}^2$

Answer 1

The correct option is C $6kg{m}^2$

Given , M.I. of a thin uniform ring about an axis passing through the centre and perpendicular to plane is $4kg{m}^2=m{r}^2.$

Using Perpendicular axix theorem,

M.I. of a thin uniform ring about an axis passing through the centre and in the plane of the ring is $2kg{m}^2=\frac{1}{2}m{r}^2.$

Now, Using Parallel axix theorem,

M.I. of ring about an axis tangent to the ring and in a plane of the ring$\frac{1}{2}m{r}^2+m{d}^2=\frac{3}{2}m{r}^2=\left(\frac{3}{2}\right)4kg{m}^2=6kg{m}^2.$

Therefore, C is correct option.