A block of mass m is attached to one end of a mass less spring of spring constant k. the other end of spring is fixed to a wall the block can move on a horizontal rough surface. The coefficient of friction between the block and the surface is `mu` then the compession of the spring for which maximum extension of the spring becomes half of maximum compression is .

Options

A. `(2mg mu)/(k)`
B. `(mg mu)/(k)`
C. `(4mg mu)/(k)`
D. None of these

Answer

C

Explanation

`E_(i)-E_(f) =` Work done againt fricion
`:. 1/2kx^(2)-1/2K(x/2)^(2) =mu mg (x+x/2)`
`:. x=(4mu mg)/k`.