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Question

In the given picture both pulley and string are massless. Pulley is frictionless. Find the acceleration of mass 2m



A

g

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B

2g

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C

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D

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Solution

The correct option is B


Constraint relation:-

If 2m moves x down then m will move x up. Pretty obvious right

And hence if 2m has acceleration a downwards then m will have acceleration a upwards. At times if might become not that obvious. So we have a technique.

(1) Take reference point (Here the pulley)

(2) (1)Measure the length of the string by assigning variables.

Here: - Let length of string connected to block of mass 2m be x1 

Total length of the string is l = x1 + x2

Assume acceleration of the blocks between which you want constraint relation.

dldt=dx1dt+dx2dt0=V1+V2

 dx1dt=V1 as x1 is being decreased by upward acceleration a1

 dx2dt=V2 as x2 is being increased by downward acceleration a2

(dldt=0 as l is constant) Differentiating once again

0 = -a1+a2 

a1 = +a2

So if 2m block goes down with an acceleration a then block m goes up with same acceleration a

Draw free body drawing write eqn

T -mg = ma     ____(i)             2mg - T = 2ma            ___(ii)

Adding (i) and (ii)

mg = 3ma

a=mg3m=g3


Physics

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