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Question

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle α 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 C 45
Let us first draw the FBD of the string-pulley system given in the question.

Let T be the tension in the strings over the pulleys.

For equilibrium of both blocks of mass m :
T=mg ....(i)

For equilibrium of block of mass 2 m
2 mg=2Tcosα
Tcosα=12mg ..(ii)
(from the figure, by symmetry, the angle made by the other section of the string with the vertical should also be α)

Using (i) and (ii), we get
cosα=12
α=45

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