Two bodies A and B have masses 20 kg and 5 kg respectively . Each one is acted upon by a force of 4kg -wt . If they acquire the same kinetic energy in times `t_(A)andt_(B)` , then the ratio `(t_(A))/(t_(B))`is

Options

A. `(1)/(2)`
B. 2
C. `(2)/(5)`
D. `(5)/(6)`

Answer

B

Explanation

`a_(1)=(F)/(m_(1))=(4xx10)/(20)=ms^(-2)`
`a_(1)=(F)/(m_(2))=(4xx10)/(5)=8ms^(-2)`
Given that , `K_(A)=K_(B)` ie , `(1)/(2)m_(1)v_(1)^(2)=(1)/(2)m_(2)v_(2)^(2)`
or `m_(1)(u+a_(1)t_(1))^(2)=m_(2)(u+a_(2)t_(2))^(2) " " (becausev=u+at)`
or`m_(1)a_(1)^(2)t_(1)^(2)=m_(2)a_(2)^(2)t_(2)^(2) " " (becauseu=0)` or
or `(t_(1))/(t_(2))=sqrt((m_(2))/(m_(1))xx(a_(2)^(2))/(a_(1)^(2)))` or
`=sqrt((5)/(20)xx((8)^(2))/((2)^(2)))=sqrt((5xx64)/(20xx4))=2`