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Question

A spring -block system is as shown in the figure. Blocks 2 kg and 3 kg are at rest. Coefficient of friction between 2 kg and incline is

A
23
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B
12
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C
13
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D
13
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Solution

The correct option is A 23
Since the 3 kg block tends to pull down due to gravity, 2 kg block tends to move up. Hence, friction on 2 kg will be down the plane.
FBD of 2 kg block:


As system is at rest, From FBD we can deduce that,
N=2gcosθ .....(1)
T=2gsinθ+μN .......(2)
From (1) and (2) we get ,
T=2gsinθ+μ(2gcosθ) .......(3)
FBD of 3 kg block:

From the figure we can deduce that , T=3g .......(4)
From (3) and (4) we get ,
3g=2g(sinθ+μcosθ)
32=sin30+μcos30
μ=23
Thus, option (a) is the correct answer.

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