Question

The gravitaional field in a region due to a certain mass distribution is given by $\overrightarrow{E}=(4\hat{i}-3\hat{j})\text{N/kg}.$ The work done by the field in moving a particle of mass $2\text{kg}$ from $\left(2\text{m,}1\text{m}\right)$ to $\left(\frac{2}{3}\text{m,}2\text{m}\right)$ along the line $3x+4y=10$ is

• A. $-\frac{25}{3}\text{J}$
• B. $-\frac{50}{3}\text{J}$
• C. $\frac{25}{3}\text{J}$
• D. $\text{zero}$

Answer 1

The correct option is B $-\frac{50}{3}\text{J}$

$W=m(\overrightarrow{E}\cdot \overrightarrow{d})=m[\overrightarrow{E}\cdot (\overrightarrow{r_2}-\overrightarrow{r_1})]$
$W=2[(4\hat{i}-3\hat{j})\cdot (\frac{2}{3}\hat{i}+2\hat{j}-2\hat{i}-\hat{j})]$
$W=2[(4\hat{i}-3\hat{j})\cdot (-\frac{4}{3}\hat{i}+\hat{j})]$
$W=2\left[4\right(-4/3)-3(1\left)\right]=2\frac{(-16-9)}{9}=-\frac{50}{9}$