The system is released from rest. Derive the relation between acceleration of the masses involved.

a_{2} = 2 a_{1}

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a_{2} = a_{1}

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a_{1} = 2 a_{2}

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a_{1} = 4 a_{2}

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Solution

The correct option is A $a_{2} = 2 a_{1}$

Rope constraint:
$l_{2} + 2 l_{1} = c o n s t a n t$
Double differentiating above equation
$\Rightarrow \frac{d^{2} l_{2}}{d t^{2}} + 2 \frac{d^{2} l_{1}}{d t^{2}} = 0$
Here
$\frac{- d^{2} l_{2}}{d t^{2}} = a_{2}; \frac{d^{2} l_{2}}{d t^{2}} = a_{1}$
$- a_{2} + 2 a_{1} = 0 \Rightarrow a_{2} = 2 a_{1}$

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