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The sphere at P is given a downward velocity v0and swings in a vertical plane at the end of a rope of length l=1mattached to a support at O. The rope breaks at angle 300from horizontal, knowing that it can withstand a maximum tension equal to three times the weight of the sphere. Then the value of v0 will be :

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a

g2ms-1

b

2g3ms-1

c

3g2 ms-1

d

g3ms-1

answer is C.

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Detailed Solution

when it travels 300 from the initial position the loss in potential energy is mgl sin300= mg/2 l=1mtension in the string in the displaced positionT= mv2l+mg cos600=3mg mv2=3mg-mgcos600= 5mg2 (12mv2=5mg4applying conservation of energy 12mv02 +mgl2= 12mv2=5mg4mv02=5mg2-mg=3mg2 v0=3g2

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The sphere at P is given a downward velocity v0and swings in a vertical plane at the end of a rope of length l=1mattached to a support at O. The rope breaks at angle 300from horizontal, knowing that it can withstand a maximum tension equal to three times the weight of the sphere. Then the value of v0 will be :