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Question

In the following figure, the pulley P1 is fixed and the pulley P2 is movable. If W1=W2=100 N, what is the the value of AP2P1? The pulleys are light and frictionless.



A
30
loader
B
60
loader
C
90
loader
D
120
loader

Solution

The correct option is D 120
Since a single string has been used to connect W1, P1, P2 let the tension in the entire string be T.
Applying the equilibrium condition on block with weight W1 in vertical direction, we get:
T=W1=100 N  ....(i)

Further let AP2P1=2θ, since the vertical line passing through centre of pulley P2 acts as its angle bisector.

F.B.D



Resolving tension in horizontal and vertical direction and since pulley P2 is massless we get :
2Tcosθ=T1, where T1 is the tension in string connecting block and pulley P2
Again applying equilibrium condition on block,
T1=W2
2Tcosθ=W2     ...(ii)
From Eq.(i)
2W1cosθ=W2
W1=W2=100 N
cosθ=12
θ=60
AP2P1=2θ=120

Physics

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