A system consists of three masses and connected by a string passing over a pulley P. The mass hangs freely and and are on a rough horizontal table (the coefficient of friction = ). The pulley is frictionless and of negligible mass. The downward accel

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Solution

Q.
A system consists of three masses $m_{1}, m_{2}$ and $m_{3}$ connected by a string passing over a pulley P. The mass $m_{1}$ hangs freely and $m_{2}$ and $m_{3}$ are on a rough horizontal table (the coefficient of friction = $μ$ ). The pulley is frictionless and of negligible mass. The downward acceleration of mass $m_{1}$ is

(Assume $m_{1} = m_{2} = m_{3} = m$ ) [2014]

1 $\frac{g (1 - g μ)}{9}$

2 $\frac{2 g μ}{3}$

3 $\frac{g (1 - 2 μ)}{3}$

4 $\frac{g (1 - 2 μ)}{2}$

Ans.
(3)

Force of friction on mass $m_{2} = μ m_{2} g$

Force of friction on mass $m_{3} = μ m_{3} g$

Let $a$ be the common acceleration of the system.

$∴$    $a = \frac{m_{1} g - μ m_{2} g - μ m_{3} g}{m_{1} + m_{2} + m_{3}}$

Here,   $m_{1} = m_{2} = m_{3} = m$

$∴$    $a = \frac{m g - μ m g - μ m g}{m + m + m}$

$= \frac{m g - 2 μ m g}{3 m}$

$= \frac{g (1 - 2 μ)}{3}$

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