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Question

Two blocks A and B of masses m & 2m respectively are held at rest such that the spring is in natural length. Find out the accelerations of blocks A and B respectively just after release (pulley, string and spring are massless).
1507145_5def7d3165d64ba483fb99822cf9dff8.png


A
g,g
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B
g3,g3
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C
0, 0
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D
g,0
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Solution

The correct option is B $$\dfrac{g}{3} \downarrow, \dfrac{g}{3} \uparrow$$
Let us assume that the block A of mass m is tied to the spring. However at $$t=0s$$, the spring is not compressed or extended.

Let $$T$$ be the tension in the string going over pulley.   Just after releasing the force on block A, both blocks move with the same acceleration. The tension is same in the rope on both sides.  The equations of motion for both blocks are: 
 $$ T - m g = m a$$
$$ 2mg - T = 2m a$$
So  $$ mg = 3 m a   =>  a = g/3$$
So at t = 0, block A moves up initially with an acceleration $$g/3$$ and block $$B$$ moves down with acceleration$$ g/3.$$
Hence the option $$B$$ is the correct answer.


Physics

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