Question

The potential energy $\varphi$ in joule of a particle of mass $1$ $kg$ moving in x-y plane obeys the law, $\varphi =3x+4y$. Here $x$ and $y$ are in metre. If the particle is at rest at ($6m,8m$) at time $t=0$, then, the work done by conservative force on the particle from the initial position to the instant when it crosses the x-axis is:

• A. $25J$
• B. $-25J$
• C. $50J$
• D. $-50J$

Answer 1

Answer: (C)

$50J$

We have,
Potential energy,
$\varphi =3x+4y$
At rest,
position of the particle $(6,8)$ at time $t=0$
$\therefore {\varphi }_{rest}=3\left(6\right)+4\left(8\right)=50J$
This should be the minimum amount of work done by conservative force on the particle from the initial position to the instant when it crosses the x-axis