A time dependent force F=3t (F in Newton and t in second) acts on three blocks m1,m2 and m3 kept in contact on a rough ground as shown. Co-efficient of friction between blocks and ground is 0.4. If m1,m2 and m3 are 3 kg, 2 kg and 1 kg respectively, the time after which the blocks started to move is (g=10ms−2)

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

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a

$\frac{4}{3} \sec$

b

$\frac{8}{3} \sec$

c

$8 \sec$

d

$4 \sec$

answer is B.

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Detailed Solution

$f = μ (m_{1} + m_{2} + m_{3}) g = 0.4 (3 + 2 + 1) \times 10 = 24 N$

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

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A time dependent force F=3t (F in Newton and t in second) acts on three blocks m1,m2 and m3 kept in contact on a rough ground as shown. Co-efficient of friction between blocks and ground is 0.4. If m1,m2 and m3 are 3 kg, 2 kg and 1 kg respectively, the time after which the blocks started to move is (g=10ms−2)