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Question

Minimum horizontal force F required to keep the smaller block stationary with respect to the bigger block as shown in the figure is :


A
(Mm)gμ
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B
(M+m)gμ
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C
Mgμ
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D
mgμ
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Solution

The correct option is B (M+m)gμ
Let us suppose that, acceleration of the system is a, then
Fnet=mtotala
a=FM+m ...... (1)


Taking ground as the frame of reference.
F.B.D of smaller block:


On applying F=ma along horizontal direction,
N=ma=mFM+m... (2) [from (1)]
Now, on applying F=ma along vertical direction,
fmg=0 [No acceleration along vertical direction]
f=mg
In limiting case,
Friction (f)=μN
μN=mg
μmFM+m=mg [from (2)]
F=(M+m)gμ
Minimum horizontal force required is (M+m)gμ to keep the smaller block stationary with respect to the bigger block.

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