A body of mass 1 kg is tied with a thread and is whirled in a vertical circal of radius 50 cm with a speed of `500 cm*s^(-1)` . What will be the tension in the thread at the highest and the lowest positions of the body ?

Explanation

Speed of the body at every point on the circular path is the same and its value ,`v=500 cm*s^(-1) =5m*s^(-1)`.
So, at every point on the circular path,
centripetal force, `F=(mv^2)/r =(1xx(5)^2)/(0.5)=50 N`
Weight of the body `=mg=1xx9.8=9.8 N`
At the highest position , the tension in the thread `(T_1)` and weight of the body both act downwards, and tohether they provide the necessary centripetal force. Hence,
`F=mg+T_1 or, T_1=F-mg=50-9.8=40.2N`
At the lowest position , the tension in the thread `(T_2)` acts in the upward direction but the weight acts downwards, and hence, in this case, `(T_2-mg)` provides the necessary centripetal force.
So, `T_2-mg=F or, T_2=F+mg=50+9.8=59.8N`.