Two equal masses are connected by a light string which is made to pass over a smooth, light pulley. The percentage of mass to be transferred from one body to another so that the bodies move by 50m in 5s is nearly (take $\text{g}=10{\text{ms}}^{-2}$ )        

Case 1 : Given${\text{m}}_1={\text{m}}_{\text{2}}=\text{m}$

$\text{a}=\text{0}$

Case 2 : When certain mass${\text{m}}^{\text{1}}$ is Removed from A and added to B then

$\text{a}=\left[\frac{\left(\text{m}+{\text{m}}^{\text{1}}\right)-\left(\text{m}-{\text{m}}^{\text{1}}\right)}{\left(\text{m}+{\text{m}}^{\text{1}}\right)+\left(\text{m}-{\text{m}}^{\text{1}}\right)}\right]\text{g}$  

$\text{a}=\frac{{\text{m}}^{\text{1}}}{\text{m}}\text{g}$

We know$\text{S}=\text{Ut}+\frac{1}{2}{\text{at}}^{\text{2}}$

$\text{t}=5\sec$

$50=0+\frac{1}{2}\frac{{\text{m}}^{\text{1}}}{\text{m}}\times 10\times 25$

$\frac{{\text{m}}^{\text{1}}}{\text{m}}=\frac{50}{125}$

$\frac{{\text{m}}^{\text{1}}}{\text{m}}=\frac{2}{5}$

$\therefore \%$ of fraction of mass removed

$\frac{{\text{m}}^{\text{1}}}{\text{m}}\times 100=\frac{2}{5}\times 100$

$=40\%$