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Constrained Motion : Intuitive Approach

In the figure...

Question

In the figure, assume that there is negligible friction between the blocks and the table. Compute the acceleration of $m_{1}$ in $m / s^{2}$ , if acceleration of $m_{2}$ due to force $F$ is $5 m / s^{2}$ and $m_{1} = 300 g, m_{2} = 200 g$

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Solution

$∵$ Pulley is connected directly to mass $m_{2}$
$∴ a_{m_{2}} = a_{p}$ (acceleration of pulley)
Now we know
$a_{p} = \frac{a_{B} + a_{C}}{2}$
$\Rightarrow 5 = \frac{0 + a_{C}}{2}$ (because AB is fixed)
$\Rightarrow a_{C} = 10 m / s^{2}$
And it is equal to acceleration of mass $m_{1}$
i.e $a_{m_{1}} = 10 m / s^{2}$

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