First slide

Connected bodies

Question

Two weights $w_{1}$ and $w_{2}$ 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

Moderate

A

$\frac{4 w_{1} w_{2}}{w_{1} + w_{2}}$
B

$\frac{2 w_{1} w_{2}}{w_{1} + w_{2}}$
C

$\frac{w_{1} w_{2}}{w_{1} + w_{2}}$
D

$\frac{w_{1} w_{2}}{2 (w_{1} + w_{2})}$

Solution

$T = \frac{2 m_{1} m_{2}}{(m_{1} + m_{2})} (g + a) = \frac{2 m_{1} m_{2} (g + g)}{m_{1} + m_{2}}$
$\Rightarrow T = \frac{4 m_{1} m_{2}}{m_{1} + m_{2}} g = \frac{4 w_{1} w_{2}}{w_{1} + w_{2}}$

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