Masses of two bodies are 1kg and 4kg respectively. If their kinetic energies are in `2:1` proportion, ratio of their speeds is ……………

Options

A. `2sqrt(2):1`
B. `1:sqrt(2)`
C. `1:2`
D. `2:1`

Answer

A

Explanation

`m_(1)=1kg,m_(2)=4kg,(K_(1))/(K_(2))=2:1`
Now, `(K_(1))/(K_(2))=((1)/(2)m_(1)v_(1)^(2))/((1)/(2)m_(2)v_(2)^(2))=((1kg)v_(1)^(2))/((4kg)v_(2)^(2))`
`therefore (2)/(1)=(1)/(4)(v_(1)^(2))/(v_(2)^(2)) therefore (v_(1)^(2))/(v_(2)^(2))=(8)/(1) therefore (v_(1))/(v_(2))=(2sqrt(2))/(1)`