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Question

If pulleys shown in the diagram are smooth and massless and a1 & a2 are acceleration of blocks of mass 4 kg and 8 kg respectively. Then find a2.


A
g/3
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B
2g/3
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C
4g/3
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D
2g
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Solution

The correct option is B 2g/3

For 8 kg
2T=8a2 ...(1)
For 4 kg block
4gT=4a1 ...(2)
From the diagram, we can observe if 4 kg moves with acceleration a1 then block of 8 kg will move with acceleration a1/2.
Hence, a2=a1/2 ...(3)
Substituting in equations (i) & (ii), we get

add eq(1) and 2*eq(2)

a1=8g12=2g3

a1=2g/3

using eq(3) we get
a2=g/3


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