A 500g ball moves in a vertical circle on a 102cm long string. If the speed at the top is 4.0m/s, then the speed at the bottom will be 7.5m/s.

A) What is the ball's weight?

B) What is the tension in the string when the ball is at the top?

C) What is the tension in the string when the ball is at the bottom?

Explanation:

ball's weight = mg = .5 x 9.8 = 4.9 N.

If T₁ be tension at the top , centripetal force provided at the top

= mg + T₁ = 4.9 + T₁

4.9 + T₁ = m v² / r , v = velocity at the top , r = radius of circular path = 1.02 m

4.9 + T₁ = .5 x 4² / 1.02

4.9 + T₁ = .5 x 4² / 1.02

=  T₁ = 7.843 - 4.9 = 2.943 N

If T₂ be tension at the bottom , centripetal force provided at the bottom

=  T₂ - mg  =  T₂ - 4.9

 T₂ - 4.9 = m v² / r , v = velocity at the bottom , r = radius of circular path = 1.02 m

 T₂ - 4.9= .5 x 7.5² / 1.02

T₂ - 4.9 = .5 x 7.5² / 1.02

 T₂ =  32.47  N