A time dependent force $F = 3 t$ ( $F$ in Newtons and $t$ in seconds) acts on three blocks $m_{1}, m_{2}$ and $m_{3}$ kept in contact on a rough ground as shown. Coefficient of friction between blocks and ground is $0.4$ . If $m_{1}, m_{2}$ and $m_{3}$ are $3 k g, 2 k g$ and $1 k g$ respectively, the time after which the blocks start to move is $(g = 10 m s^{- 2})$

4 s e c

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8 s e c

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\frac{8}{3} s e c

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\frac{4}{3} s e c

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Solution

The correct option is B $8 s e c$

Taking the blocks as one system.
Friction force on the system, $f = μ (m_{1} + m_{2} + m_{3}) g = 0.4 (3 + 2 + 1) \times 10 = 24 N$

To move the blocks,
$F \geq f \Rightarrow 3 t \geq 24, \Rightarrow t \geq 8 s$

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