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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 sec
If 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 ms2
From equation (1), we get
t=7.5 sec
Hence, the correct answer is (b).

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