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Laws Of Motion

Question
CBSEENPH11017022

A body of mass m lying on a frictionless table has a light inextensible string attached to it. The string passes through a hole on the surface of table and has a body of mass M suspended from its other end. The system is kept in equilibrium by revolving the body on the table in a circle of radius r. Find the speed of the body to keep the system in equilibrium.

Solution
Let v be the speed of mass m.

As the svstem is in equilibrium, therefore
               T = Mg                            ...(1)
and         T equals fraction numerator m v squared over denominator r end fraction                         ...(2)
From (1) and (2), 
               fraction numerator m v squared over denominator r end fraction space equals space M g
So,  space space v equals square root of fraction numerator M r g over denominator m end fraction end root, is the required speed of the body to be in equilibrium.