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Question

# Assuming that the surface is frictionless and strings are inextensible, find the acceleration of the block of mass 2m shown in the figure.

A
g6
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B
g3
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C
g4
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D
g2
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Solution

## The correct option is A g6Let the acceleration of pulley, block of mass m and 2m be ap, a and a2 respectively. So, from the method of intercept we have l1+l2=constant Differentiating w.r.t time, we get equation in the form of velocity i.e .l1+.l2=0 Again differentiating w.r.t time, we get equation in the form of acceleration i.e ⇒ ap+ap−a=0 ⇒a=2ap ........... (1) Also, l3+l4=constant Double differentiating w.r.t time, we get equation in the form of acceleration i.e .l3+.l4=0 ⇒−ap+a2=0 ⇒a2=ap...............(2) From (1) & (2), we can say that a=2a2 Now, from the FBD of m, Pulley and 2m we have, From the FBD of block of mass m, T−mgsinθ=m(2a2) As θ=30∘ ⇒ T−mg2=2ma2..........(3) From FBD of pulley, T′=2T From the FBD of block of mass 2m, 2mg−T′=2ma2⇒ 2mg−2T=2ma2 ⇒ mg−T=ma2...........(4) From (3) & (4), we have mg−mg2=3ma2⇒a2=g6 Thus, acceleration of the mass 2m is g6

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