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Question

The pulleys and strings shown in the figure are smooth and massless. For the system to remain in equilibrium, the angle θ should be:


A
0
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B
30
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C
45
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D
60
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Solution

The correct option is B 30
The tension (T) in both strings i.e connecting block B, A and B,C will be equal due to symmetry of arrangement.


For the system to be in equilibrium, all the three masses A,B,C should be in equilibrium.

From equilibrium of mass A and C:
T=mg.......(i)

Resolving the tension T acting on B in horizontal and vertical direction. The net force in horizontal direction is balanced on mass B.

Applying equilibrium condition for mass B in vertical direction :

3mg=2Tcosθ...........(ii)

From Eq. (i) and (ii):
3mg=2(mg)cosθ
32=cosθ
θ=30

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