A plank having mass M is placed on smooth horizontal surface. Block of mass m is placed on it coefficient of friction between block and plank is ${\mathrm{\mu }}_0+{\mathrm{kx}}^2$, where k is constant and x is relative displacement between block and plank. A force F is applied on block where F = at, where a = 10; t is in second. Find ${\mathrm{t}}_0$ when relative motion will occur between block and plank

• A

  ${\mathrm{\mu }}_0\mathrm{M}+\frac{{\mathrm{\mu }}_0{\mathrm{M}}^2}{\mathrm{m}}$

• B

  ${\mathrm{\mu }}_0\mathrm{m}+\frac{{\mathrm{\mu }}_0{\mathrm{M}}^2}{\mathrm{m}}$

• C

  ${\mathrm{\mu }}_0\mathrm{m}+\frac{{\mathrm{\mu }}_0{\mathrm{m}}^2}{\mathrm{M}}$

• D

  ${\mathrm{\mu }}_0\mathrm{M}+\frac{{\mathrm{\mu }}_0{\mathrm{m}}^2}{\mathrm{M}}$