Q: A spring placed horizontally on a rough horizontal surface is compressed against a block of mass m placed on the surface so as to store maximum energy in the spring. If the coefficient of friction between the block and the surface is μ , the potential energy stored in the spring is

(A) μ^{2}m^{2}g^{2}/2k

(B) 2μm^{2}g^{2}/k

(C) μ^{2}m^{2}g/2k

(D) 3μ^{2}mg^{2}/k

Sol: For equilibrium of the block

F_{max} – μmg = 0

F = μmg

$ \displaystyle U = \frac{1}{2}kx^2 = \frac{k^2 x^2}{2 k}$

$ \displaystyle U = \frac{k^2 x^2}{2 k} = \frac{(kx)^2}{2k}$

$ \displaystyle U = \frac{F^2}{2 k} $

$ \displaystyle U = \frac{\mu^2 m^2 g^2}{2 k} $