Two uniform solid spheres have the same mass,but one has twice the radius of the other.The ratio of the larger sphere's moment of inertia about a central axis to that of the smaller sphere is
A)4/5.
B)8/5.
C)1/2.
D)2.
E)4.

Question

Quizplus · Accepted Answer

The moment of inertia of a solid sphere is given by the expression,
I = (2/5) * M * R^2
where,
I = moment of inertia
M = mass
R = radius

Let the smaller sphere have the radius 'r' and the larger sphere have the radius '2r'.
Both the spheres have the same mass, so let the mass be represented by 'm'.

Moment of inertia of the smaller sphere will be,
I_small = (2/5) * m * r^2

Moment of inertia of the larger sphere will be,
I_large = (2/5) * m * (2r)^2 = (2/5) * m * 4r^2 = (8/5) * m * r^2

To find the ratio of I_large to I_small, we divide the two equations,
I_large / I_small = [(8/5) * m * r^2] / [(2/5) * m * r^2] = (8/5) / (2/5) = 4

Therefore, the ratio of the larger sphere's moment of inertia about a central axis to that of the smaller sphere is 4.

Two Uniform Solid Spheres Have the Same Mass,but One Has