Physics - NLM Question with Solution | TestHub

Let the string length be $l_1+l_2=L$; differentiating twice, $a_1+a_2=-2g$ (accelerations of the weights relative to the ground, with the pulley accelerating up at $g$): $\frac{d^2{l}_1}{d{t}^2}+\frac{d^2{l}_2}{d{t}^2}=0\Rightarrow (g+a_1)+(g+a_2)=0$ ...(1)

$w_1-T=\frac{w_1{a}_1}{g}$ ...(2)

$w_2-T=\frac{w_2{a}_2}{g}$ ...(3)

Solving (1), (2) and (3): $T=\frac{4w_1{w}_2}{w_1+w_2}$.