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Elastic Potential Energy

If U1, U2, U3...

Question

If $U_{1}, U_{2}, U_{3}$ represent the potential energy differences for moving a particle from $A$ to $B$ along three different paths $1, 2 & 3$ (as shown in the figure) in the gravitational field of point mass $m$ , find the correct relation between $U_{1}, U_{2} & U_{3}$ .

A

U_{1} = U_{2} = U_{3}

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B

U_{1} > U_{2} > U_{3}

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C

U_{1} < U_{2} < U_{3}

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D

U_{1} > U_{2} < U_{3}

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Solution

The correct option is A $U_{1} = U_{2} = U_{3}$
Gravitational potential energy is path independent because gravitational force is conservative in nature.
Thus, $U_{1} = U_{2} = U_{3}$

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