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Potential Energy of an Object at a Height

If W 1, W...

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}

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B

W_{1} = W_{2} = W_{3}

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C

W_{1} < W_{2} < W_{3}

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D

W_{2} > W_{1} > W_{3}

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Solution

The correct option is B $W_{1} = W_{2} = W_{3}$
In a conservative field work done does not depend on the path, and gravitational field is a conservative field.
$∴ W_{1} = W_{2} = W_{3}$

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