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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 g3From constrained condition and using method of intercept we have, ..L1+..L2+..L3=0 ⇒−a1+a2+a2=0⇒a1=2a2……(1) From FBD of masses m and 2m we have force equations as T=ma1...........(i) 2mg−2T=2ma2............(ii) From eq (1), we get Tm=2[g−Tm] 3Tm=2g⇒T=2mg3 ∴ a2=[g−Tm]=[g−2g3] ⇒a2=g3 Thus, the acceleration of 2m mass is g3

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