A spring 40 mm long is stretched by the application of a force . If 10 N force required to stretch the spring through 40 mm is `……..`

Options

A. 23 J
B. 68 J
C. 84 J
D. 8 J

Answer

D

Explanation

Force applied F = 10 N
stretching in the spring x = 1 mm = `0.001 ` m
spring constant `k = F/x =10/(1xx10^(-3)) = 10^(4)`
Now spring is stretching through a distance `x_(1) = 40 mm = 0.04 m `
The force required to stretch is through `x_(1)` is
`F_(1) =kx_(1)`
` :. ` The work done by the force
`W = 1/2 kx_(1)^(2) =1/2 kx_(1) xxx_(1)`
` = 400/2 xx0.004`
= 8 J