Question

two bodies have their masses m1/m2 =1/3 and their kinetic energies ke1/ke2 =2/3 . the ratio of their velocities(a) 2:1​

Answer 1

$\large \underline \bold{Given} :-$

$\rm{\small \underline{for \: two \: bodies}}$

$\rm{\: \: \: \: \: \: \: \: \: \: \: \: \: \: mass \: ratio \: = \dfrac{m\displaystyle_{1}}{m\displaystyle_{2}} \: = \: \dfrac{1}{3}}$

$\rm{\: \: \: kinetic \: energies \: ratio \: = \: \dfrac{KE\displaystyle_{1}}{KE\displaystyle_{2}} \: = \: \dfrac{2}{3}}$

$\large \underline \bold{To \: Find}:-$

$\rm{\: \: \: \: \: \: \: \: velocities \: ratio \: = \dfrac{V\displaystyle_{1}}{V\displaystyle_{2}} \: = \: \mathord{?}}$

$\large \underline \bold{Using \: formula :-}$

$\rm{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \large \boxed{KE = \dfrac{1}{2} m v^{2}}}$

$\large \underline \bold{answer :-}$

$\rm{\: \: \: \: \: \: \: \: \: \: \: \: \dfrac{KE\displaystyle_{1}}{KE\displaystyle_{2}} \: = \: \dfrac{m\displaystyle_{1}\times V\displaystyle_{1}^{2}}{m\displaystyle_{2}\times V\displaystyle_{2}^{2}}}$

$\rm{\: \: \: \: \: \: \: \: \: \: \: \: \dfrac{KE\displaystyle_{1}}{KE\displaystyle_{2}} \: = \: \bigg(\dfrac{m\displaystyle_{1}}{m\displaystyle_{2}}\bigg)\times \bigg(\dfrac{V\displaystyle_{1}}{V\displaystyle_{2}}\bigg)^{2}}$

$\rm{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \dfrac{2}{\cancel{3}} \: = \: \dfrac{1}{\cancel{3}}\times \bigg(\dfrac{V\displaystyle_{1}}{V\displaystyle_{2}}\bigg)^{2}}$

$\rm{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \dfrac{2}{1} \: = \: \bigg(\dfrac{V\displaystyle_{1}}{V\displaystyle_{2}}\bigg)^{2}}$

$\rm{\: \: \: \: \: \: \:\bigg(\dfrac{V\displaystyle_{1}}{V\displaystyle_{2}}\bigg) \: = \: \dfrac{\sqrt{2}}{1}}$