Question

If two circular rings A and B are of same mass but of radii r and 2r respectively, then the moment of inertia about an axis passing through C.G. and perpendicular to its plane, of A is ______.

Options

• same as that of B

• twice that of B

• four times that of B

• `1/4` that of B

Answer 1

If two circular rings A and B are of same mass but of radii r and 2r respectively, then the moment of inertia about an axis passing through C.G. and perpendicular to its plane, of A is `bbunderline(1/4 "that of B")`.

Explanation:

For ring A:

Radius = r

I_A = Mr²    ...(i)

For ring B:

Radius = 2r

I_B = M(2r)²    ...(ii)

Equations (i) and (ii) we get,

`(Mr^2)/(M(2r)^2) = (I_A)/(I_B)`

`(I_A)/(I_B) = 1/4`

`I_A = (I_B)/4`