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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 A 4.5 m/s2 down the plane
The 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 P7:802T=ma7T=40 N as m=0
For the block: The acceleration of the block a is given as
10gsin30°408=10a
10×10×125=10a
a=4.5 m/s2 down the plane


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