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Question

Two blocks (1 and 2) of equal mass m are connected by an ideal string (see figure below) over a frictionless pulley. The blocks arc attached to the ground by springs having spring constants k1 and k2 such that k1>k2.
Initially, both springs are unstretched. The block 1 is slowly pulled down a distance x and released. Just after the release the possible values of the magnitudes of the acceleration of the blocks a1 and a2 can be.

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A
either (a1=a2=(k1+k2)x2m) or
(a1=k1xmganda2=k2xm+g)
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B
(a1=a2=(k1+k2)x2m) only
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C
(a1=a2=(k1k2)x2m) only
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D
either (a1=a2=(k1k2)x2m) or
(a1=a2(k1k2)x(k1+k2)mg)
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Solution

The correct option is A either (a1=a2=(k1+k2)x2m) or
(a1=k1xmganda2=k2xm+g)
For Mass 1
T+k1mg=ma1
For mass 2
k2x+mgT=ma2
if after release the string remains tight then a1=a2
so a1=a2=(k1+k2)x2m
Now if string becomes loose the T=0
So a1=k1xmg
a2=k2xm+g

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