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=10m/s2.)
A
2.25m/s2 towards left
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B
2.25m/s2 towards right
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C
9m/s2 towards left
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D
9m/s2 towards right
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Solution
The correct option is B2.25m/s2 towards right The given system can be reframed as shown
FBDs of the pulleys and the block
For P7:80−2T=ma7⇒T=40N As pulley is massless, m=0 For the block: The acceleration of the block a is given by 10gsin30°−408=10a ⇒a=4.5m/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=−2.25m/s2 Thus, ap=−2.25m/s2 to left or 2.25m/s2 to right.