First slide

Two block problem

Question

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 (Take, g = 10 ms^-2) [EAMCET 2013]

Moderate

A

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

$\frac{14}{4}, 3$
C

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

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

Solution

We know that, $F - f = m a$
Here, for small body, $a_{1} = \frac{20 - 0.2 \times 3 \times 10}{3}$
$\Rightarrow a_{1} = \frac{14}{3} {ms}^{- 2}$
Similarly, $0.2 \times 3 \times 10 = 10 \times a_{2}$
$\Rightarrow a_{2} = \frac{6}{10} = 0.6 {ms}^{- 2}$

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