Two springs of spring constants `1500N//m` and `3000N//m` respectively are streched by the same force. The potential energy gained by the two springs will be in the ratio

Options

A. `4:1`
B. `1:4`
C. `2:1`
D. `1:2`

Answer

C

Explanation

`U_(1)/U_(2)=((1)/(2)k_(1)x_(1)^(2))/((1)/(2)k_(2)x_(2)^(2))=((k_(1)x_(1))^(2))/(k_(1))xx(k_(2))/((k_(2)x_(2))^(2))`
`=(F^(2))/(k_(1))xx(k_(2))/(F^(2))=(k_(2))/(k_(1))=(3000)/(1500)=2:1`.