A spring, which is initially in its unstretched condition, is first stretched by a length x and then again by a further length x. The work done in the first case is `W_(1)` and in the second case is `W_(2)`.

Options

A. `W_(2)= 4W_(1)`
B. `W_(2)=W_(1)`
C. `W_(2)=2 W_(1)`
D. `W_(2)= 3W_(1)`

Answer

D

Explanation

In the first case, its potential energy `U=(1)/(2)Kx^(2) and W_(1)=(1)/(2)Kx^(2)`, where K is the force constant of the spring. When it is stretched through a total dis"tan"ce 2x, its potential energy `U_(2)=(1)/(2)K(2x)^(2)=(1)/(2)K(4x^(2))`
`therefore W_(2)=U_(2)-U_(1)=(1)/(2)K(4x^(2)-x^(2))`
`therefore W_(2)=3((1)/(2)Kx^(2))=3W_(1)`