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Question

A system consists of block A and B of same mass 5 kg and connected to the pulley as shown in figure. Find the relative acceleration with which they will move?
(Take g=10 m/s2)

A
8 m/s2
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B
5 m/s2
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C
4 m/s2
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D
16 m/s2
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Solution

The correct option is D 16 m/s2
Static friction between two blocks,
f2smax=μ2s×5g=30 N
Since f2smax<F, the blocks will move and hence, friction will be kinetic.
Drawing FBD of both blocks

Friction between A and B,
f2k=μ2k(5g)=0.4(50)=20 N

Both will move with the same acceleration in opposite direction, (because they are connected by a string)

Let us write equations of motion for both blocks A and B.
For Block B:
Tf2k=mBa
i.e T20=5a(1)
For Block A:
FTf2k=mAa
120T20=5a(2)

Adding (1) and (2), 80=10a
or a=8 m/s2
As both the block are moving in upposite direction. So, the relative acceleration is 16 m/s2

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