Two blocks A and B each of mass m = 2kg are placed at the ends of a plank of mass $M = 8 k g$ and length $l = 8 m$ which is placed on a smooth horizontal surface. A horizontal force F = 34 N is applied to the plank, then choose the correct option(s). $(g = 10 m / s^{2})$
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Frictional force acting on the block B is 4 N

Time after which the two blocks will collide is 4 s

Frictional force acting on the block A is 6 N

Time after which the two blocks will collide is 2 s

answer is A, B, D.

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Detailed Solution

We can find no slipping between A and M
$\Rightarrow a_{B} = 2 m / s^{2}, a_{A + B} = 3 m / s^{2} f_{A} = m a_{A} = 2 (3) = 6 N, f_{B} = μ m g = 0.2 \times 20 = 4 N$

A and B will collide after t :
$- 8 = \frac{1}{2} (2 - 3) t^{2} \Rightarrow t^{2} = 16 \Rightarrow t = 4 \sec$