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Pulley

Two unequal m...

Question

Two unequal masses of $1 k g$ and $2 k g$ are connected by an inextensible light string passing over a smooth pulley as shown in the figure. A force $F = 20 N$ is applied on $1 k g$ block. Find the acceleration of either block. $(g = 10 m / s^{2})$ in $m / s^{2}$

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Solution

The given system can be represented as shown

Total downward force on $1 k g$ mass = $F + g = 20 + 10 = 30 N$
And, on $2 k g$ mass = $2 g = 20 N$
Hence, $1 k g$ mass will accelerate downwards
For $1 k g$ mass we have,
$30 - T = a$ ........... (1)
For $2 k g$ mass we have,
$T - 20 = 2 a$ ...........(2)
From (1) & (2) we get
$10 = 3 a \Rightarrow a = \frac{10}{3} m / s^{2}$

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