Question

If $W_1$, $W_2$ and $W_3$ represent the work done in moving a particle from $A$ to $B$ along three different paths $1$, $2$ and $3$ (as shown in fig) in the gravitational field of the point mass $'m'$. Find the correct relation between $'W'_1$, $'W_2'$ and $'W_3'$

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

Answer 1

Answer: (C)

$W_1 = W_2 = W_3$

Answer 2

Gravitational force is a conservative froce. As we know that the work done by a conservative force is independent of the path followed and depends only on the end points of the motion. Since in the given pattern $w_{1}, w_{2}$ and $w_{3}$ have the same end point $A$ and $B$ as shown in the figure below,