• # question_answer An object of mass m is travelling on a horizontal surface. There is a coefficient of kinetic friction $\mu$ between the object and the surface. The object has speed v when it reaches at $x=0$ and later encounters a spring. The object compresses the spring, stops and then recoils and travel in opposite direction. When object reaches $x=0$ on its return trip, it stops. From this information the spring constant k is A) $\frac{2{{\mu }^{2}}m{{g}^{2}}}{{{v}^{2}}}$ B) $\frac{4{{\mu }^{2}}m{{g}^{2}}}{{{v}^{2}}}$ C) $\frac{3{{\mu }^{2}}m{{g}^{2}}}{{{v}^{2}}}$ D) $\frac{16{{\mu }^{2}}m{{g}^{2}}}{{{v}^{2}}}$

 $\frac{1}{2}m{{v}^{2}}=(\mu mg)x$and$\frac{1}{2}k{{x}^{2}}=\frac{1}{2}m{{v}^{2}}$ On solving, we get $k=\frac{4m{{\mu }^{2}}{{g}^{2}}}{{{v}^{2}}}$