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

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=(2 m 1 m 2/ m 1+ m 2) (C) m 3=√ m 1 m 2 (D) m 3=(4 m 1 m 2/ m 1+ m 2)

Tardigrade Admin · Accepted Answer

Tension in lower string T =(2 m 1 m 2/ m 1+ m 2) g If m 3 is at rest then 2 T = m 3 g ⇒ m 3=(4 m 1 m 2/ m 1+ m 2)

Q. 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

$m_{3} = m_{1} + m_{2}$

$m_{3} = \frac{2 m _{1} m _{2}}{m _{1} + m _{2}}$

$m_{3} = m_{1} m_{2}$

$m_{3} = \frac{4 m _{1} m _{2}}{m _{1} + m _{2}}$

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

Q. Three masses m1​,m2​ and m3​ are attached to a string-pulley system as shown. All the three masses are held at rest and then released. To keep m3​ at rest, the condition is

m3​=m1​+m2​

m3​=m1​+m2​2m1​m2​​

m3​=m1​m2​​

m3​=m1​+m2​4m1​m2​​