Question

A force $\overrightarrow{F}=(3\hat{i}+4\hat{j})\text{N}$ acts on a particle moving in $x-y$ plane. Starting from the origin, the particle first goes along $x$ - axis to the point $(4\text{m, 0)}$ and then parallel to the $y$ - axis to the point $(4\text{m},3\text{m})$. The total work done by the force on the particle is

• A. $+12\text{J}$
• B. $-6\text{J}$
• C. $+24\text{J}$
• D. $-12\text{J}$

Answer 1

The correct option is C $+24\text{J}$

Given, $F=3\hat{i}+4\hat{j}$
Displacement vector $\left(\overrightarrow{s}\right)=4\hat{i}+3\hat{j}$
Work done,
$W=\overrightarrow{F}.\overrightarrow{s}$
$\Rightarrow W=(3\hat{i}+4\hat{j}).(4\hat{i}+3\hat{j})=12+12=24\text{J}$