What will be the velocity of block A in the arrangement shown ?

60 m / s

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120 m / s

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140 m / s

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200 m / s

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Solution

The correct option is C $140 m / s$
Let the downward velocity be negative and upward velocity be postive.
Pulley (1) is fixed
So $V_{B} = V_{p l a n k} = - 20 m / s$
and $V_{C} = 20 m / s$

Considering pulley (2), we can say
that $V_{D} = V_{C} = 20 m / s$
and $V_{E} = - 20 m / s$ (since the string is connected to the plank)

$V_{D} = \frac{V_{E} + V_{G}}{2}$
$\Rightarrow 20 = \frac{- 20 + V_{G}}{2}$
$\Rightarrow V_{G} = 60 m / s$

Now considering pulley (3)

$V_{I} = - 20 m / s$ (connected to the plank)
and $V_{H} = V_{G} = 60 m / s$

$V_{H} = \frac{V_{I} + V_{J}}{2}$
$\Rightarrow 60 = \frac{- 20 + V_{J}}{2}$
$\Rightarrow 120 = V_{J} - 20$
$\Rightarrow V_{J} = 140 m / s$

Therefore velocity of block A $V_{A} = V_{J} = 140 m / s$

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