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Question

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


  1. 2g3
  2. g3
  3. g4
  4. g5


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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