On a plank of length 36m and mass 3kg, a small block of mass 1kg is kept as shown.
Friction coefficient between the block and the plank is 0.3 where as that between the plank and the ground is 0.6. At some instant an impulse is given to both of them such that they acquire a common initial velocity of 21 m/s as shown. After what time will be block get off the plank?

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$3 \sqrt{2} \sec$

4 sec

5 sec

$4 \sqrt{2} \sec$

answer is C.

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Detailed Solution

Acceleration of block = 3m / s², Acceleration of plank = -7m / s² After 3 sec, the plank will come to rest. In 3 sec, the block will move $\frac{1}{2} \times 4 \times 3 \times 3 = 18 m$ relative to the plank. Now, let the block will cover remaining 18m relative to plank in next t seconds.
$12 t - \frac{1}{2} \times 3 t^{2} = 18$ , $8 t^{2} - t^{2} = 10 \Rightarrow t = 2 \sec$
Total time after which the block will get off the plank, $t_{0} = 3 + 2 = 5 \sec$