First slide

Connected bodies

Question

In the figure, pulleys are smooth and strings are massless, m₁ = 1 kg and $m_{2} = \frac{1}{3} kg$ To keep m3 at rest, mass m₃ should be

Difficult

A

1 kg
B

$\frac{2}{3} k g$
C

$\frac{1}{4} k g$
D

2 kg

Solution

m₃ is at rest. Therefore,
2T = m₃ g …(i)
Further, if m₃ is at rest, then pulley P is also at rest.
Writing equations of motion, m₁g $-$ T = m₁a …(ii)
T $-$ m₂g = m₂a …(iii)
Solving Eqs. (i), (ii) and (iii), we get
m₃ = 1 kg

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