Question

A uniform solid sphere of radius r is placed on a smooth horizontal surface is pulled by a constant force

Answer 1

• The distance traveled by the sphere during the time it makes one complete revolution is 4πR/3.

According to the question a solid sphere is lying on the smooth horizontal surface as shown in the figure.

Taking moment of inertia about the center of hollow sphere we will get-

Before that suppose the radius of sphere is R and the force by which it is pulled if F. So

F×R = 2/3 MR² α

⇒ α = 3F/2MR

Again we know that,

2π = 1/2 α t² (From Ф = ω₀t + 1/2 α t² )

⇒ t² = 8πMR/ 3F

⇒ a = F/M

⇒ X = 1/2 a t²

= 1/2 × F/M × 4π × 2MR/3F

= 4πR/3