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A block of mass 1 kg is placed over a plank of mass 2 kg. The length of the plank is 2m. Coefficient of friction between the block and the plank is 0.5 and the ground over which plank is placed is smooth. A constant force F = 30 N is applied on the plank is horizontal direction. Find the time after which the block will separate from the plank is $(g = 10 {m/s}^{2})$

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0.0075 s

7.5 s

0.75 s

0.12 s

answer is A.

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Detailed Solution

N due to upper block

= 1 \times g = 10 N

Frictional force on upper surface of 2 kg block

$= μ \times 1 \times g = 0 .5 g = 5N$

Let acceleration of 2 kg block is ${'a}_{1}'$

The and acceleration of 1 kg block w.r.t to 2kg block is ${'a}_{21}'$

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${2a}_{1} = F - f$

$a_{1} = \frac{F - f}{2} = \frac{30 - 5}{2} = \frac{25}{2}$

For 1 kg block; $1 \times a_{21} = 1 \times a_{1} - 5 = \frac{15}{2}$

Using $S = ut + \frac{1}{2} {at}^{2}$

$2 = 0 + \frac{1}{2} a_{21} t^{2}$

$t = \sqrt{\frac{4}{a_{21}}} = \sqrt{\frac{4}{(\frac{5}{2})}}$

$t = \sqrt{\frac{8}{15}} = 0.75 \sec$

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