Question

The moment of inertia of solid sphere is 20 kg-mabout the diameter. The moment of inertia about an
tangent will be
(A™) 70 kg-ma
(B) 35 kg-m2
(C) 50 kg-m?
(D) 20 kg-m​

Answer 1

Answer:

Option (A) 70 kg-m²

Explanation:

Moment of inertia of a Solid Sphere of mass M and radius R, about its centre is given by

$\boxed{I=\frac{2}{5}MR^2}$ .......... (1)

Here I is given as, $I=20$ kg-m²

If we shift the axis from the centre to the tangent (i.e. at a distance R), from parallel axis theorem, the moment of inertia will be

$I'=I+MR^2$

From eq (1)

$MR^2=\frac{5I}{2}$

Therefore,

$I'=I+\frac{5I}{2}$

$\implies I'=\frac{7I}{2}$

$\implies I'=\frac{7\times 20}{2}$

$\implies I'=70$ kg-m²

Hope this helps.