Question

An object is displaced from position vector ${\overrightarrow{r}}_1=(2\hat{i}+3\hat{j})\text{m}$ to ${\overrightarrow{r}}_2=(4\hat{i}+6\hat{j})\text{m}$ under the action of a force $\overrightarrow{F}=(3x^2\hat{i}+2y\hat{j})N$. Find the work done by this force.

• A. $17\text{J}$
• B. $83\text{J}$
• C. $10\text{J}$
• D. $80\text{J}$

Answer 1

The correct option is B $83\text{J}$

Wprk done by variable force$W=\underset{r_1}{\overset{r_2}{\int }}\overrightarrow{F}.\overrightarrow{dr}=\underset{r_1}{\overset{r_2}{\int }}(3x^2\hat{i}+2y\hat{j}).(dx\hat{i}+dy\hat{j}+dz\hat{k})$
$=\underset{r_1}{\overset{r_2}{\int }}(3x^{2}dx+2ydy)=[x^3+y^2{]}_{(2,3)}^{(4,6)}=83\text{J}$