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Pulley

In the figure...

Question

In the figure shown, find the velocity of the $3 k g$ mass after $10 s$ if the system is released from rest at $t = 0$ . (Take $g = 10 m / s^{2}$ )

30 m / s

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40 m / s

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50 m / s

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70 m / s

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Solution

The correct option is B $40 m / s$
The FBD of the blocks are shown in the below figure

So, from the FBD we have
$7 g - T = 7 a$ ......(i)
$T - 3 g = 3 a$ .......(ii)
From the eq (i) & (ii), we get
$a = \frac{4 g}{10} = 4 m / s^{2}$
From equation of motion we have,
$v = u + a t$
$\Rightarrow v = 0 + 4 \times 10 = 40 m / s$

OR

$a = \frac{(Supporting force - opposing Force)}{Total mass}$
$= \frac{7 g - 3 g}{10} = 4 m / s^{2}$
From equation of motion we have,
$v = u + a t$
$\Rightarrow v = 0 + 4 \times 10 = 40 m / s$

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