A certain spring that obeys Hook's law is stretched by an external agent. The work done in stretching the spring by `10 cm` is `4 J` . How much additional work is required to stretch the spring an additional `10 cm`?

Explanation

Here, `W=4J, x_(1)=10cm =(1)/(10)m`
`K=?W=?x_(2)=10+10=20cm =(1)/(5)m`
From `W=(1)/(2)Kx_(1)^(2)`
`4=(1)/(2)K((1)/(10))^(2),K=800N//m`
Additional work done `=(1)/(2)Kx_(2)^(2)-(1)/(2)Kx_(1)^(2)`
`=(1)/(2)K(x_(2)^(2)-x_(1)^(2))`
`W=(1)/(2)xx800[((1)/(5))^(2)-((1)/(10))^(2)]`
`=400((1)/(25)-(1)/(100))=400xx(3)/(100)=12J`