In the position shown in figure, the spring is at its natural length. The block of mass `m` is given a velocity `v_0` towards the vertical support at `t=0`. The coefficient of friction between the block and the surface is given by `mu=alphax`, where `alpha` is a positive constant and x is the position of the block from its starting position. The block comes to rest for the first time at x, which is

Options

A. (a) `v_0sqrt((m)/(k+alphamg))`
B. (b) `v_0sqrt(m/k)`
C. (c) `v_0sqrt((m)/(alphag))`
D. (d) None of these

Answer

A

Explanation

According to the work-energy theorem,
`1/2mv_0^2=mg alpha underset0oversetx int dx+1/2kx^2`
Solving we get, `x=v_0sqrt((m)/(k+alphamg))`