When the sphere is rotting about a diameter, the particles

present on the surface of the sphere revolves in concentric

circles. So, centripetal accelerations exist.

(a) is not true.

The particles present on the surface of the sphere takes equal

time to complete one revolution

So, (c) is not true.

We have the linear speed

That means the particles at different radius

will have different linear speed.

So, (d) is not true.

Now for the particles following diametric path r becomes 0. So, v= 0.

For v is not changing, linear acceleration is zero. (b) is correct.