Question

An object is displaced from point $A(2,1)m$ to a point $B(0,4)m$ under the influence of a force $\overrightarrow{F}=-2x\hat{i}+3\hat{j}.$ The workdone by this force is

• A. $22\text{J}$
• B. $-6\text{J}$
• C. $13\text{J}$
• D. $-12\text{J}$

Answer 1

The correct option is C $13\text{J}$

Given variable force $\overrightarrow{F}=-2x\hat{i}+3\hat{j}$
Displacement vector $\overrightarrow{ds}=dx\hat{i}+dy\hat{j}$
workdone $\left(W\right)=\int \overrightarrow{F}.\overrightarrow{ds}={\int }_{(2,1)}^{(0,4)}(-2x\hat{i}+3\hat{j}).(dx\hat{i}+dy\hat{j})$
$W={\int }_{(2,1)}^{(0,4)}-2xdx+3dyW=-x^2{|}_{\left(2\right)}^{\left(0\right)}+3y{|}_{\left(1\right)}^{\left(4\right)}$
$W=-(0^2-2^2)+3(4-1)=13\text{J}$