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Three springs A, B and C each of force constant $K$ , are connected at O. The other ends of B and C are connected to massless rings which can slide on smooth sliders as shown in the diagram. A massless pan is hanging from other end of the spring A. When a block of mass m is placed in the pan. The amount of work done by the gravity on block system after it stops vibrating is $\frac{N m^{2} g^{2}}{K} .$ The spring C does not sag. Find ‘ $N$ ’.

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Detailed Solution

The system will adjust in such a way by sliding the spring C remains unstretched and spring A and B remains vertical. Thus, effective force constant is given by $\frac{1}{K'} = \frac{1}{K} + \frac{1}{K} K' = \frac{K}{2}$

There is no effect of spring C.

$K' x = m g$

$x = \frac{2 m g}{K}, W = m g . x = m g . \frac{2 m g}{k} = \frac{2 m^{2} g^{2}}{k}$

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