The system is shown in the figure and the man is pulling the rope from both sides with constant speed u. Then the speed of the block will be. (M moves vertical)

\frac{3 u}{4}

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\frac{3 u}{2}

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\frac{u}{4}

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None of these.

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Solution

The correct option is D $\frac{3 u}{4}$
A man is pulling the rope from both sides with constant speed u.

According to figure,

Applying of virtual work method

$\sum \to T \cdot \to V = 0$

Let the velocity of mass M be v in upward direction.

Now,

$- T u - u \frac{T}{2} + 2 T v = 0$

$\frac{- 2 T u - T u}{2} = - 2 T v$

$- 3 T u = - 4 T v$

$v = \frac{3 u}{4}$

Hence, the speed of the block will be $\frac{3 u}{4}$ .

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