JEE MainPhysicsModerate

A small sphere tied to a string of length 0.8 m is describing a
vertical circle so that the maximum and minimum tensions in the string
are in the ratio 3: 1. The fixed end of the string is at a height of
5.8 m above ground. Find the velocity of the sphere at the lowest
position. (Take g = 10 m/s^2)

Show answer and solution

let u and v be the speeds of the sphere at the bottom and the
top positions and m be themass
[IMAGE] Radius of circle = length of string =r=0.8 m
[IMAGE] =tension at the bottom or the maximum tension
[IMAGE] =tension at the top or the minimum tension
Using conservation of energy
KE from bottom to the top =Gain in GPE
Using equations (1) and (2) we get[IMAGE] TOPIC:Circular motion
SUB TOPIC:Vertical circle