Question bank/JEE Main/Physics

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 $\mu_{0} + kx$,where k is constant and x is relative
displacement of block w.r.t. plank. A force F is applied on block where
F=at, where a=10; t is in second. Find$t_{0}$ to when relative motion
will occur between block and plank (use $g = 10m/s^{2}$).

A$\mu_{0}M + \frac{\mu_{0}M^{2}}{m}$B$\mu_{0}m + \frac{\mu_{0}M^{2}}{m}$C$\mu_{0}m + \frac{\mu_{0}m^{2}}{M}$D$\mu_{0}M + \frac{\mu_{0}m^{2}}{M}$

Show answer and solution▾

Let at time t_o relative motion will occur.
[IMAGE] $\mu_{0}mg = Ma$..... (1)
[IMAGE] $10t_{0} - \mu_{0}mg = ma$..... (2)
From (1) and (2);
$t_{0} = \mu_{0}m + \frac{\mu_{0}m^{2}}{M}$

Source: Grass-G / P-18 Physics paper 27 Nov Third.docx