Moment of Inertia | MCQs

Explanation

 The moment of inertia of a solid sphere is (2/5)MR^2, where M is the mass and R is the radius.

This formula applies when the axis of rotation passes through the center of the sphere. 

Explanation

To calculate the moment of inertia of the Earth about its diameter, we can use the formula for the moment of inertia of a sphere:

I = (2/5)MR^2

where:

I = moment of inertia

M = mass of the Earth (10^25 kg)

R = radius of the Earth (diameter/2 = 12800 km / 2 = 6400 km = 6.4 × 10^6 m)

Plugging in the values, we get:

I = (2/5) × 10^25 kg × (6.4 × 10^6 m)^2

= (2/5) × 10^25 kg × 4.096 × 10^13 m^2

= 1.6384 × 10^38 kg m^2

≈ 1.64 × 10^38 kg m^2

Explanation

Using the Parallel Axis Theorem:

I = I_CM + Md^2

where I_CM = MR^2/2 and d = R (radius)

I = MR^2/2 + MR^2

= 3/2 MR^2

Explanation

The moment of inertia depends on the mass of the object,

how the mass is distributed relative to the axis of rotation,

and the axis of rotation itself,

but it does not depend on the angular velocity.