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Question

In the figure shown, all pulleys are massless and the strings are light and inextensible. What is the acceleration of the pulley P4? (All surfaces are smooth and take g=10 m/s2.)

A
2.25 m/s2 towards left
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B
2.25 m/s2 towards right
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C
9 m/s2 towards left
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D
9 m/s2 towards right
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Solution

The correct option is B 2.25 m/s2 towards right
The given system can be reframed as shown

FBDs of the pulleys and the block

For P7:802T=ma7T=40 N
As pulley is massless, m=0
For the block: The acceleration of the block a is given by
10gsin30°408=10a
a=4.5 m/s2
For constrained condition, let pulley P4 move to the left with ap
..L11+..L10+..L9+..L8+..L7=0
a+0+0+ap+ap=0
ap=a2=4.52=2.25 m/s2
Thus, ap=2.25 m/s2 to left
or 2.25 m/s2 to right.

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