Question

Four identical solid spheres each of mass m and radius r are fixed at four corners of a light square frame of side length 4r such that centres of spheres coincide with corners of square. The moment of inertia of 4 spheres about an axis perpendicular to the plane of frame and passing through its centre is

Answer 1

Answer:

Distance of the center of the spheres from the axis is d=2

2

R

Now the MI of a solid sphere about its axis is 2MR

2

/5

Using the parallel axis theorem, the MI about the given axis is 2MR

2

/5+Md

2

=2MR

2

/5+M(2

2

R)

2

=2MR

2

/5+8MR

2

=42MR

2

/5

So total MI of system is 4×42MR

2

/5=168MR

2

/5