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Question

In the arrangement shown in figure. There is a fricion force between the block of masses m and 2m. Block of mass 2m is kept on a smooth horizontal plane. The mass of suspended block is m. Block A is stationary with respect to block of mass 2m. The minimum value of coefficient of fricion betwen A and B is


A
12
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B
12
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C
14
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D
13
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Solution

The correct option is C 14
The FBDs of the block can be shown as below



Given, Block A and B are moving together and the surface is smooth.
Let coefficient of friction between A and B be μ
Then, acceleration of the system is
asystem=(Supporting force-Opposing force)Total mass
mg04m=g4

For block A not to slip on B, we have
f=m(asystem)
μmg=m(g4)
μ=14

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