Q. Two weights $\omega_{1}$ and $\omega_{2}$ are suspended from the ends of a light string passing over a smooth fixed pulley. If the pulley is pulled up at an acceleration $g$, the tension in the string will be
A) $\frac{4\omega_{1}\omega_{2}}{\omega_{1} + \omega_{2}}$
B) $\frac{2\omega_{1}\omega_{2}}{\omega_{1} + \omega_{2}}$
C) $\frac{\omega_{1}\omega_{2}}{\omega_{1} + \omega_{2}}$
D) $\frac{\omega_{1}\omega_{2}}{2(\omega_{1} + \omega_{2})}$
Explanation
(a) $T = \frac{2m_{1}m_{2}}{\left( m_{1} + m_{2} \right)}(g + a) = \frac{2m_{1}m_{2}(g + g)}{m_{1} + m_{2}}$
$\Rightarrow T = \frac{4m_{1}m_{2}}{m_{1} + m_{2}}g = \frac{4\omega_{1}\omega_{2}}{\omega_{1} + \omega_{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.