Question

An object is displaced from point $A(1,0)m$ to a point $B(0,4)m$ under the influence of a force $\overrightarrow{F}=-2\hat{i}+5\hat{j}.$ The workdone by this force is

• A. $-18\text{J}$
• B. $20\text{J}$
• C. $22\text{J}$
• D. $-22\text{J}$

Answer 1

The correct option is C $22\text{J}$

Given force $\overrightarrow{F}=-2\hat{i}+5\hat{j}$
Displacement vector $\overrightarrow{ds}=dx\hat{i}+dy\hat{j}$
workdone $\left(W\right)=\int \overrightarrow{F}.\overrightarrow{ds}={\int }_{(1,0)}^{(0,4)}(-2\hat{i}+5\hat{j}).(dx\hat{i}+dy\hat{j})$
$W={\int }_{(1,0)}^{(0,4)}-2dx+5dyW=-2x{|}_{\left(1\right)}^{\left(0\right)}+5y{|}_{\left(0\right)}^{\left(4\right)}$
$W=-2(0-1)+5(4-0)=22\text{J}$