Question

A particle moves under the effect of a force F = Cx from x = 0 to x = x₁. The work done in the process is ______.

Options

• `Cx_1^2`

• `1/2Cx_1^2`

• Cx₁

• Zero

Answer 1

A particle moves under the effect of a force F = Cx from x = 0 to x = x₁. The work done in the process is `bbunderline(1/2Cx_1^2)`.

Explanation:

Given: F = Cx 

Particle moves from: 

x = 0 to x = x₁

Work done by variable force:

W = `intF dx`

= `int_0^(x_1) Cx dx`   

Substitute force (F = Cx)

= `Cint_0^(x_1) xdx`

= `C[x^2/2]_0^(x_1)`

= `(C x_1^2)/2`

= `1/2Cx_1^2`