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Question

In the given figure, the coefficient of friction between m1 and m2 is μ and m2 and horizontal surface is zero. Choose the correct option.


A
If F>μm1g, then relative acceleration is found between m1 and m2
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B
If F<μm1g, then no relative acceleration is found between m1 and m2
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C
If F>μm1g, then both bodies move togther
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D
(a) and (b) are correct
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Solution

The correct option is B If F<μm1g, then no relative acceleration is found between m1 and m2
The FBDs of the blocks are as shown




Let us consider that there is no relative acceleration between m1 and m2
From FBD we get
Ff=m1a (on mass m1) ... (1)
f=m2a (on mass m2) ... (2)
f=μsm1g (f=μsN1) ... (3)
F=(m1+m2)a

From (1), (2) and (3)
F=(m1+m2)μsm1gm2
F=μsm1g(1+m1m2)
This is maximum possible force so that there is no relative acceleration between m1 and m2
Or, If F<μm1g, then no relative acceleration is found between m1 and m2

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