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Potential Energy of an Object at a Height

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 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 $W_{1} = W_{2} = W_{3}$
Work done under a conservative force such as gravitation is only dependent on displacement between final & initial points $W = \to F . \to s$ where $\to s$ is displacement, hence regardless of distance covered by $441, 2$ and $3$ Hence work done from $A t o B$ are equal $\Rightarrow_{1} = W_{2} = W_{3}$

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