Q. Two bodies of masses $m_{1}$ and $m_{2}$ are connected by a light, inextensible string which passes over a frictionless pulley. If the pulley is moving upward with uniform acceleration $g$, then the tension in the string is
A) $\frac{4m_{1}m_{2}}{m_{1} + m_{2}}g$
B) $\frac{m_{1}m_{2}}{{4m}_{1}m_{2}}g$
C) $\frac{m_{1}m_{2}}{m_{1} + m_{2}}g$
D) $\frac{m_{1} - m_{2}}{m_{1} + m_{2}}g^{2}$
Explanation
(a) When the system accelerates upwards, the effective value of acceleration due to gravity is given by
$f^{'} = g + a = g + g = 2g$
Now, $T = \frac{2\left( m_{1} \right)(m_{2})}{m_{1} + m_{2}}$(2g) or $T = \frac{4m_{1}m_{2}}{m_{1} + m_{2}}$g
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.