Question

A block is resting on a horizontal plank. Coefficient of friction between block and plank is $‘{\mu }^{\prime }$. The plank begins to move in x – direction with velocity given by $u=a{t}^2$, ‘t’ being time and ‘a’ being constant. The time at which block start sliding is $\frac{\mu g}{na}$. Then the value of n is

Answer 1

$v=a{t}^2$

acceleration, $\frac{dv}{dt}=2at$

Block will start sliding when

$m\frac{dv}{dt}\ge \mu mg\Rightarrow \frac{dv}{dt}\ge \mu g$

$\Rightarrow 2at\ge \mu g$

$\Rightarrow t\ge \frac{\mu g}{2a}$

$\therefore n=2$