A light rope is attached to a block with mass $4 \; kg$ that rests on a frictionless, horizontal, and surface. The horizontal rope passes over a frictionless pulley and a block with mass $m$ is suspended from the other end. When the blocks are released, the tension in the rope is $10\;N$. Draw free body diagrams and calculate the acceleration of either block and the mass $m$ of the hanging block.

Let $m$ be the mass hanged at the other end of the rope.

Tension in the rope $(T) =10\;N$

Now for $4 \; kg$

$F = T = ma$

$a =$$ \frac{T}{m} = \frac{10}{4}$$ = 2.5\;m/s^2$

For mass $m$

$T = mg -ma$

or, $m(g -a) = T $    ⇒   $ m =$$ \frac{T}{(g - a)} = \frac{10}{10-2.5}$$ = 1.33 \; kg$

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