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Two blocks of masses 3 kg and 2 kg are placed side by side on an incline as shown in figure. A force F = 20 N is acting on 2 kg block along the incline. The coefficient of friction between the block and the incline is same and equal to 0.1. Find the normal contact force exerted by 2 kg block on 3 kg block.

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18 N

30 N

12 N

27.6 N

answer is C.

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Detailed Solution

The free-body diagrams of two blocks are shown in figure. Under the assumption that both blocks are moving together,

$F + 2 gsin 37^{\circ} + 3 gsin 37^{\circ} - f_{1} - f_{2} = 5 a$

$\begin{array}{l} where f_{1} = μ \times 3 gcos 37^{\circ} \\ For f_{2} = μ \times 2 gcos 37^{\circ} \end{array}$

$\Rightarrow a = \frac{46}{5} {ms}^{- 2}$

For 3-kg block, $N + 3 gsin 37^{\circ} - f_{1} = 3 a \Rightarrow N = 12 N$

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