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Question

Find the acceleration of the block of mass 2m as shown in the figure. (Strings are massless and inextensible)


A
2g3
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B
g3
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C
g4
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D
g5
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Solution

The correct option is B g3
From constrained condition and using method of intercept we have,
..L1+..L2+..L3=0
a1+a2+a2=0a1=2a2(1)

From FBD of masses m and 2m we have force equations as

T=ma1...........(i)
2mg2T=2ma2............(ii)
From eq (1), we get

Tm=2[gTm]
3Tm=2gT=2mg3
a2=[gTm]=[g2g3]
a2=g3
Thus, the acceleration of 2m mass is g3

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