Question

A particle moves under the effect of a force $F=Cx$ from $x=0$ to $x=x_1$. The work done in the process is

• A. $C{x}_1^2$
• B. $\frac{1}{2}C{x}_1^2$
• C. $C{x}_1$
• D. Zero

Answer 1

Answer: (B)

$\frac{1}{2}C{x}_1^2$

Here F = Cx

Work done = F.d Where d is displacement

$w={\int }_{x_1}^{x_2}F.dx$

$w={\int }_0^{x_1}Fdx$

$w={\int }_0^{x_1}cxdx$

$w=\frac{1}{2}c{x}_1^2$

Here (B) is correct answer