Question

If $W_1,W_2$ and $W_3$ represent the works done in moving a particle from $\text{A}$ to $\text{B}$ along three different paths $\text{1, 2}$ and $\text{3}$ respectively, (as shown in the figure) in the gravitational field of a point mass $m$, find the correct relation between $W_1,W_2$ and $W_3$.

• A. $W_1>W_2>W_3$
• B. $W_1=W_2=W_3$
• C. $W_1<W_2<W_3$
• D. $W_2>W_1>W_3$

Answer 1

The correct option is B $W_1=W_2=W_3$

As gravitational force is a conservative force, so the work done due to this force is independent of path.

Hence, the work done in moving a particle from $\text{A}$ to $\text{B}$ along the paths $1,2$ and $3$ in the gravitational field of mass $m$ will be same.

$\therefore W_1=W_2=W_3$

Thus, option (b) is the correct answer.