Question

An object is displaced from position vector $\overrightarrow{r_1}=2\hat{i}+3\hat{j}\left(m\right)$ to $\overrightarrow{r_2}=4\hat{j}+6\hat{k}\left(m\right)$ under a force

$\overrightarrow{F}=3x^2\hat{i}+2y\hat{j}$. Find out the work done by the force.

• A. 83 J
• B. - 1 J
• C. 37 J
• D. - 42 J

Answer 1

The correct option is B

- 1 J

$w=\underset{\overrightarrow{r_1}}{\overset{\overrightarrow{r_2}}{\int }}\overrightarrow{F}.\overrightarrow{dr}$ = $\overrightarrow{F}.\overrightarrow{dr}=(3x^2\hat{i}+2y\hat{j}).(dx\hat{i}+dy\hat{j}+dz\hat{k})$

= $3x^{2}dx+2ydy$

$\therefore w=\underset{x_1}{\overset{x_2}{\int }}3x^{2}dx+\underset{y_1}{\overset{y^2}{\int }}2ydy+\underset{z_1}{\overset{z_2}{\int }}0dz$

= $3x\frac{x^3}{3}{|}_0^2+2x\frac{y^2}{2}{|}_4^3$

= $x^3{|}_0^2+y^2{|}_3^4$

= $(0-8)+(16-9)$

= $-8+7$

= $-1J$