Question

Moment of inertia of a bar magnet of mass $m$ length $l$ breath $n$ is $I.$ then moment of inertia of another bar magnet of mass $2m$ length $2l$ breath $2b$ would be

• A. 8 I
• B. 4 I
• C. 2 I
• D. I

Answer 1

The correct option is A 8 I

Moment of inertia o a magnet of mass$m,$ length $l,$ breadth $b,$ along an axis passing through its centre is

$I=\frac{m\left(l^2+b^2\right)}{12}$---------------$\left(1\right)$

then$,$ moment of inertia of another bar magnet of mass $2m,$ length $2l$ and breadth $2b$ is

$I^{\prime }=\frac{2m\left[{\left(2l\right)}^2+{\left(2b\right)}^2\right]}{12}$

$=\frac{2m\left(4l^2+4b^2\right)}{12}$

$=\frac{8m\left(l^2+b^2\right)}{12}$

$=8I$---------------------from eq$\left(1\right)$

Hence,

option $\left(A\right)$ is correct answer.