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 figure) in the gravitational field of the point mass m. Find the correct relation between ${}^{\prime }{W}_1^{\prime }{,}^{\prime }{W}_2^{\prime }$ and ${}^{\prime }{W}_3^{\prime }$.

• 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)

$W_1=W_2=W_3$

Gravitational field is a conservative force field. Work done in a conservative field is path independent.

Hence since the start and end points are same in all three cases we can say $W_1=W_2=W_3$

Hence option $C$ is correct