Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity is [2020]

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Solution

Q.
Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity $(g)$ is [2020]

1 $g$

2 $g / 2$

3 $g / 5$

4 $g / 10$

Ans.
(3)

Given : $m_{1} = 4 kg, m_{2} = 6 kg$

From the diagram,

$T - m_{1} g = m_{1} a$ ...(i)

$m_{2} g - T = m_{2} a$ ...(ii)

Solving equation (i) and (ii)

$a = \frac{(m_{2} - m_{1}) g}{m_{2} + m_{1}} = \frac{(6 - 4) g}{10} = \frac{2}{10} g = \frac{g}{5}$

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