Q.

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 

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a

8:1

b

7:1

c

4:1

d

1:7

answer is B.

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Detailed 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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