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 with acceleration $g$ , the tension in the string will be

• 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. $\frac{w_{1} \, w_{2}}{2 \left(w_{1} - w_{2}\right)}$

Answer 1

Answer: (A)

For solving the problem, we assume that observer is situated in the frame of pulley (non - inertial reference frame).

$m_{1}g=w_{1}$
$m_{2}g=w_{2}$
From force diagram [a],
$T-m_{2}a_{0}-w_{2}=m_{2}a$
Or $T-m_{2}g-w_{2}=m_{2}a$ $\left(\because \, a_{0} = g\right)$
Or $T-2w_{2}=m_{2}a$ .....(i)
From force diagram [b],
$m_{1}a_{0}+w_{1}-T=m_{1}a$
Or $m_{1}g +w_{1}-T=m_{1}a$ $\left(\because \, \, a_{0} = g\right)$
Or $2W_{1}-T=m_{1}a$ ......(ii)
From equations (i) and (ii),
$T=\frac{4 w_{1} \, w_{2}}{w_{1} + w_{2}}$