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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

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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 ms−2

From equation (1), we get

t=7.5 sec

Hence, the correct answer is (b).

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 ms−2

From equation (1), we get

t=7.5 sec

Hence, the correct answer is (b).

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