Question

The point of application of the force $(-2,4,7)$ is displaced from the point $(3,-5,1)$ to the point $(5,9,7)$, but the force is suddenly halved when the point of application moves half the distance.The work done by the force is

• A. $70$
• B. $70.5$
• C. $75$
• D. $75.5$

Answer 1

The correct option is B $70.5$

Resultant vector of two points is given by

$\overline{r}=(2,14,6)$

We know
$w=F\cdot \frac{\overline{r}}{2}+\frac{F}{2}\cdot \frac{\overline{r}}{2}$
$=\frac{3}{4}\overline{F}\cdot \overline{r}=\frac{3}{4}(-4+56+42)$
$=\frac{47}{2}\times 3$
$=\left(23.5\right)\times 3$
$=70.5$