question_answer

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?

A) \[2mg\]

B) \[mg\]

C) \[\frac{3mg}{2}\]         

D) \[4mg\]

Correct Answer: A

Solution :

[a] \[F=2T\sin \theta \] or \[T\sin \theta =\frac{F}{2}\] \[T\sin \theta +N=mg\] \[\Rightarrow N=mg-T\sin \theta \] For no loss of contact: N>0 \[\Rightarrow mg-T\sin \theta >0\] \[\Rightarrow mg-\frac{F}{2}>0\] \[\Rightarrow F<2mg\] So \[{{F}_{\max }}=2mg\]