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Work Energy Theorem Application

Two blocks of...

Question

Two blocks of masses $M_{1}$ and $M_{2}$ are connected by spring of constant $K$ . The spring is initially compressed and the system is released from rest at $t = 0$ second. The work done by spring on the blocks $M_{1}$ and $M_{2}$ be $W_{1}$ and $W_{2}$ respectively by time t. The speeds of both the blocks at time t are non zero. Then the value of $\frac{W_{1}}{W_{2}}$ equals to

A

\frac{M_{1}}{M_{2}}

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B

\frac{M_{2}}{M_{1}}

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C

{(\frac{M_{1}}{M_{2}})}^{2}

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D

{(\frac{M_{2}}{M_{1}})}^{2}

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Solution

The correct option is B $\frac{M_{2}}{M_{1}}$
$W_{1} = \frac{1}{2} M_{1} V_{1}^{2} W_{2} = \frac{1}{2} M_{2} V_{2}^{2} M_{1} V_{1} = M_{2} V_{2} \frac{W_{1}}{W_{2}} = \frac{M_{1} V_{1}}{M_{2} V_{2}} . \frac{V_{1}}{V_{2}} = \frac{M_{2}}{M_{1}}$

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