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Q.

A 3 kg block is placed over a 10 kg block and both are placed on a smooth horizontal surface. The coefficient of friction between the blocks is 0.2. If a horizontal force of 20 N is applied to 3 kg block, accelerations of the two blocks in ms^–2 are (g = 10ms^–2)

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a

$\frac{13}{4}, 0.6$

b

$\frac{14}{3}, 0.6$

c

$\frac{14}{3}, 3$

d

$\frac{13}{4}, 3$

answer is D.

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Detailed Solution

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$\begin{array}{l} Maximum frictional force on the upper block = {μm}_{u} g = 0.2 \times 3 \times 10 = 6 N \\ As applied force is greater than 6 N \\ a_{L} = \frac{{μm}_{u} g}{m_{L}} = 0.2 \frac{3}{10} \times 10 = 0.6 m / s^{2} \\ a_{u} = \frac{F - {μm}_{u} g}{m_{u}} = \frac{20 - 0.2 \times 3 \times 10}{3} = \frac{14}{3} m / s^{2} \end{array}$

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