JEE Main · PhysicsHard

$A block of mass $m$ is attached to a spring of constant $k$ and is placed on a rough horizontal surface with coefficient of friction $\mu$. If the block is released from rest at a distance $x_0$ from the equilibrium position, what is the total distance traveled by the block before it comes to rest permanently?$

Show correct answer & step-by-step solution

Correct answer: A — $\frac{kx_0^2}{2\mu mg}$

Solution

The work done by friction over the total distance

d

must equal the initial potential energy stored in the spring,

\frac{1}{2} k x_{0}^{2}

. Since the work done by friction is

W = μ m g d

, equating this to

\frac{1}{2} k x_{0}^{2}

gives

d = \frac{k x _{0}^{2}}{2 μ m g}