Question

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

A
4.5 m/s2 down the plane
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B
4.5 m/s2 up the plane
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C
5 m/s2 down the plane
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D
5 m/s2 up the plane
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Solution

## The correct option is C 4.5 m/s2 down the planeThe given system can be framed as shown FBDs of the pulleys and the blocks are as shown. Let T be the tension in the string connected to pulley P7. Let a be the acceleration of block m. For P7:80−2T=ma7⇒T=40 N as m=0 For the block: The acceleration of the block a is given as 10gsin30°−408=10a 10×10×12−5=10a a=4.5 m/s2 down the plane

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