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Question

# Two blocks A and B of mass 2 kg and 4 kg are placed one over the other. A horizontal force F=2t, which varies with time is applied on the upper block. If coefficient of friction between blocks A and B is 0.5 and horizontal surface is smooth. Then assuming t is in seconds, the total time upto which both blocks will move together without slipping over each other is

A
5 sec
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B
7.5 sec
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C
10 sec
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D
12.5 sec
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Solution

## The correct option is B 7.5 secIf common maximum acceleration is ′a′ then, (mA+mB)a=F ⇒(2+4)a=2t ⇒3a=t ……(1) For block B, we have fL=mB×a ⇒0.5×2×10=4a ⇒a=2.5 ms−2 From equation (1), we get t=7.5 sec Hence, the correct answer is (b).

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