A gravitational field is present in a region, and a mass is shifted from $A$ to $B$ through different paths as

Question

A gravitational field is present in a region, and a mass is shifted from $A$ to $B$ through different paths as shown. If $W_1$, $W_2$ and $W_3$ represent the work done by the gravitational force along their respective paths, then:

Accepted Answer

1. **Identify the Nature of Force:** Gravitational force is a conservative force [Class 11 Physics, Ch 6, Sec 6.8].
2. **Apply Property of Conservative Forces:** The work done by a conservative force depends only on the initial and final positions of the object and is independent of the path taken to go from one point to another.
3. **Conclusion:** Since the initial point ($A$) and final point ($B$) are the same for all three paths, the work done by gravity is identical for all paths.
   $$ W_1 = W_2 = W_3 $$

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