Question

two bodies of equal masses move with uniform velocity v and 4 respectively find the ratio of their Kinetic energies​

Answer 1

CORRECT QUESTION :

Two bodies of equal masses move with uniform velocity v and 4v respectively. find the ratio of their Kinetic energies.

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{K.E_{1}:K.E_{2}=1:16}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies m_{1} = m_{2} = m \\ \\ \tt: \implies Velocity( v_{1}) =v \\ \\ \tt: \implies Velocity( v_{2}) =4v \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Ratio \: of \: kinetic \: energy = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies \frac{K.E_{1}}{K.E_{2}} = \frac{ \frac{1}{2} m_{1}{ v_{1}}^{2} }{\frac{1}{2} m_{2}{ v_{2}}^{2}} \\ \\ \tt: \implies \frac{K.E_{1}}{K.E_{2}} = \frac{2 m_{1} { v_{1}}^{2} }{2 m_{2} v_{2}^{2} } \\ \\ \tt \circ \: m_{1} = m_{2 } = m \\ \\ \tt: \implies \frac{K.E_{1}}{K.E_{2}} = \frac{m v_{1}^{2} }{ mv_{2}^{2} } \\ \\ \tt: \implies \frac{K.E_{1}}{K.E_{2}} = \frac{ {(v)}^{2} }{ {(4v)}^{2} } \\ \\ \tt: \implies \frac{K.E_{1}}{K.E_{2}} = \frac{ {v}^{2} }{16 {v}^{2} } \\ \\ \tt: \implies \frac{K.E_{1}}{K.E_{2}} = \frac{1}{16} \\ \\ \green{\tt: \implies K.E_{1} : K.E_{2} = 1 : 16}$