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 $3$, 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 $W_1=W_2=W_3$

Work done under a conservative force such as gravitation is only dependent on displacement between final & initial points $W=\overrightarrow{F}.\overrightarrow{s}$ where $\overrightarrow{s}$is displacement, hence regardless of distance covered by $441,2$ and $3$ Hence work done from $AtoB$ are equal $\Rightarrow \overrightarrow{W_1}=W_2=W_3$