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Q.

Two small spheres each of mass m connected by a string of length 2l are kept on a smooth horizontal surface. A vertical force F is applied at the middle of the string. What is maximum value of F for which the spheres do not lose contact with the surface?

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a

2mg

b

mg

c

3mg2

d

4mg

answer is A.

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Detailed Solution

F=2Tsin⁡θ or Tsin⁡θ=F2     ......(i)Tsin⁡θ+N=mg    .......(ii)⇒N=mg−Tsin⁡θ   For no loss of contact:    N>0⇒    mg−Tsin⁡θ>0⇒    mg−F2>0⇒    F<2mg So     Fmax=2mg
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