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

Answer

C

Explanation

The work done in stretching the spring by a further length x is,
`W_(2)=(1)/(2)k(2x)^(2)-(1)/(2)kx^(2)=(3)/(2)kx^(2)`
i.e., `w_(2)= 3W_(1)` [from equation (1)]