Question

Three masses $m _{1}, m _{2}$ and $m _{3}$ are attached to a string-pulley system as shown. All the three masses are held at rest and then released. To keep $m _{3}$ at rest, the condition is

• A. $m _{3}= m _{1}+ m _{2}$
• B. $m _{3}=\frac{2 m _{1} m _{2}}{ m _{1}+ m _{2}}$
• C. $m _{3}=\sqrt{ m _{1} m _{2}}$
• D. $m _{3}=\frac{4 m _{1} m _{2}}{ m _{1}+ m _{2}}$

Answer 1

Answer: (D)

Tension in lower string
$T =\frac{2 m _{1} m _{2}}{ m _{1}+ m _{2}} g$
If $m _{3}$ is at rest then $2 T = m _{3} g$
$\Rightarrow m _{3}=\frac{4 m _{1} m _{2}}{ m _{1}+ m _{2}}$