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Elastic Potential Energy

If W1, W2 a...

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 a gravitational field of point mass $m$ , then 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 D $W_{1} = W_{2} = W_{3}$
Since the gravitational field is a conservative field, hence the work done in taking a particle from one point to another in a gravitational field of path independent.
$⟹ w_{1} = w_{2} = w_{3}$

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