Question

A particle is moved from $\left(\right.0,0\left.\right)$ to $\left(\right.a,a\left.\right)$ under a force $F=\left(\right.3\hat{i}+4\hat{j}\left.\right)$ from two paths. Path $1$ is $OP$ and work done by force is $W_{1}$ and Path $2$ is $OQP$ and work done by the force in this path is $W_{2}$ . Select the correct relation between $W_{1}$ and $W_{2}$ .

• A. $W_{1}=W_{2}$
• B. $W_{1}=2W_{2}$
• C. $W_{2}=2W_{1}$
• D. $W_{2}=4W_{1}$

Answer 1

Answer: (A)

The force is constant and hence conservative.
For conservative forces, work done is independant of the path followed.
$W=\overset{ \rightarrow }{F}.\overset{ \rightarrow }{S}$ ,
Displacement is same for both the paths.
$\therefore W_{1}=W_{2}$