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Question

A pulley-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 2√3Since 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=2√3 Thus, option (a) is the correct answer.

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