Question

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

A

g

B

2g

C

D

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+dx2dt⇒0=−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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