First slide
Conservation of mechanical energy
Question

The velocity of a body revolving in a vertical circle of radius ‘r’ at the lowest point  7gr . The ratio of maximum to minimum tensions in the string is 

Moderate
Solution

given velocity at lowest point is v12=7gr---(1) we know that vθ=v12-2gr(1-cosθ) v2=v12-2gr(1+1) substitute given v12=7gr in above equation v22=7gr-4gr v22=3gr---(2) TmaxTmin=mv12r+mgmv22r-mg substitute eqn(1) & (2) TmaxTmin=8mg2mg TmaxTmin=41  

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