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Question

A pulley mass system is shown in the figure.


The pulley and string are massless and all surfaces are frictionless. Find out the acceleration of COM of the system. [Take g=10 m/s2 and consider upward direction as positive]

A
0.4 m/s2
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B
0.2 m/s2
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C
10 m/s2
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D
5 m/s2
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Solution

The correct option is A 0.4 m/s2
FBD of the blocks are:


For Block A and B:
6gT=6a and
T4g=4a
Solving these equations,
10a=6g4g=2g
a=2×1010=2 m/s2

Acceleration of block A will be downward while acceleration of block B will be upward.
Therefore, acom=m1a1+m2a2m1+m2=6×(2)+4×26+4
acom=410=0.4 m/s2
It means COM will be accelerating downwards.

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