A gravitational field is present in a region and a mass is shifted from A to B through different paths as shown. If W₁, W₂ and W₃ represent the work done by the gravitational force along the respective paths, then

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

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

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

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

answer is A.

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Detailed Solution

In a gravitational field work done depends on displacement, not the distance travelled, because the gravitational field is conservative in nature.
So, work done depends on the initial and final position of the body.
Based on this, work done in all the three paths will be same.
So, $W_{1} = W_{2} = W_{3} .$

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