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Question

As shown in figure, all the surfaces are frictionless and the pulleys and the string are light. The magnitude of acceleration of block 2M is


A
g3
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B
g6
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C
2g3
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D
g4
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Solution

The correct option is B g6

From string constraint(string should remain taut), or length of string (l) will be constant.
l=xA+2xB+C
0=d2xAdt2+2d2xBdt2
aA=d2xAdt2 aB=d2xBdt2
0=aA+2aB

aA=2aB....(i)
F.B.D. of (A), forces shown along the inclined plane as forces to inclined plane forces will be balanced.


Applying newton's 2nd law along direction of motion:
TMgsin30=MaA
TMg2=MaA
aA=TMg2....(ii)

From F.B.D. of (B),


2Mg2T=2MaB
MgT=MaB
aB=gTM....(iii)
Adding Eq (ii) & (iii),
aA+aB=g2
2aB+aB=g2
aB=g6

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