In the position shown in figure, the spring is at its natural length. The block of mass m is given a velocity v₀ towards the vertical support at t = 0. The coefficient of friction between the block and the surface is given by $\mathrm{\mu }=\mathrm{\alpha x}$, where $\mathrm{\alpha }$ 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 

• A

  ${\mathrm{v}}_0\sqrt{\frac{\mathrm{m}}{\mathrm{k}+\mathrm{\alpha mg}}}$

• B

  ${\mathrm{v}}_0\sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$

• C

  ${\mathrm{v}}_0\sqrt{\frac{\mathrm{m}}{\mathrm{\alpha g}}}$

• D

  None of these