First slide

Constraints

Question

Two bodies of masses 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

Moderate

A

g/2
B

g/5
C

g/10
D

g

Solution

Given, $m_{1} = 4 kg, m_{2} = 6 kg and a = ?$
The free body diagram of given system is shown below
The balancing equations for given system are
$T - m_{1} g = m_{1} a$ …(i)
and $m_{2} g - T = m_{2} a$ … (ii)
Adding Eqs. (i) and (ii), we get
$m_{2} g - m_{1} g = m_{1} a + m_{2} a$
$\Rightarrow a = (\frac{m_{2} - m_{1}}{m_{1} + m_{2}}) \cdot g = (\frac{6 - 4}{4 + 6}) \times g = \frac{g}{5}$

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