Question

A variable force $F$ acts along the $x$ -axis given by $F=\left(3 x^{2} - 2 x + 1\right) \, N$ . The work done by the force when a particle of mass $100 \, g$ moves from $x=50 \, cm$ to $x=100 \, cm$ is

• A. $0.625 \, J$
• B. $6.25 \, J$
• C. $0.0625 \, J$
• D. $62.5 \, J$

Answer 1

Answer: (A)

$x_{i n i t i a l}=50 \, cm$
$x_{f i n a l}=100 \, cm$
Therefore work done by the variable force,
$W=\displaystyle \int _{x_{i n i t i a l}}^{x_{f i n a l}} F . d x$
$W=\displaystyle \int _{0.5}^{1} \left(3 x^{2} - 2 x + 1\right) d x$
$W=\left[x^{3} - x^{2} + x\right]_{0.5}^{1}$
$W=\left(1 - 0 . 5^{3}\right)-\left(1 - 0 . 5^{2}\right)+\left(1 - 0.5\right)$
$W=0.875-0.75+0.5$
$W=0.625 \, J$