Question

If ${\omega }_1,{\omega }_2$ and ${\omega }_3$ represent the work done in moving a particle from A to B along three different paths 1, 2, and 3 respectively in the presence of a gravitational field, then find the correct relation between ${\omega }_1,{\omega }_2$ and ${\omega }_3$.

• A. ${\omega }_1>{\omega }_2>{\omega }_3$
• B. ${\omega }_1<{\omega }_2<{\omega }_3$
• C. ${\omega }_1={\omega }_2={\omega }_3$
• D. None of these

Answer 1

The correct option is C

${\omega }_1={\omega }_2={\omega }_3$

Gravitational force is conservative in nature, so the work done is independent of the path taken. Hence, ${\omega }_1={\omega }_2={\omega }_3$.