Question

The work done by a force $F=-5x^4\hat{i}N$ in displacing a body from, $x=2m$ to $x=-2m$ is

• A. 6 J
• B. 8 J
• C. 64 J
• D. 0 J

Answer 1

Answer: (C)

Given, force on the body, $F=-5x^4\hat{i}N$
Body is displacing from $x=2m$ to $x=-2m$.
Hence, the work done by a force in displacing a body,
$W=\underset{x=2}{\overset{x=-2}{\int }}F\cdot dx$ or
$W=\underset{x=2m}{\overset{x=-2}{\int }}\left(-5x^4\right)dx=(-5){\left[\frac{x^5}{5}\right]}_2^{-2}$
$\Rightarrow =(-1)(-2{)}^5-(2{)}^5$
$\Rightarrow W=64J$