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Tension in a String

The blocks m2...

Question

The blocks $(m_{2} > m_{1})$ are held in such a manner that spring is unstretched initially. Consider the situation at the time of release of the block $(t = 0)$ and short time after releasing the block $(t > 0)$ . Accelerations of the blocks of masses $m_{1}$ and $m_{2}$ are $a_{1}$ and $a_{2}$ respectively

A

t = 0, a_{1} = a_{2}

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B

t = 0, a_{1} < a_{2}

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C

t > 0, a_{1} = a_{2}

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D

t > 0, a_{1} < a_{2}

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Solution

The correct option is D $t > 0, a_{1} < a_{2}$
Free body diagram of blocks
For $m_{1}$ :
$a_{1} = \frac{m_{1} g - T}{m_{1}}$
$= g - \frac{T}{m_{1}}$
For $m_{2}$ :
$a_{2} = \frac{m_{2} g - T}{m_{2}}$
$= g - \frac{T}{m_{2}}$
At $t = 0 : T = 0 \Rightarrow a_{1} = a_{2}$
At $t > 0 : T > 0 \Rightarrow a_{1} < a_{2}$

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