MHT CET · Physics · Gravitation

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 $3$ (as shown in figure) in the gravitational field of the point mass ‘ $m$ ’. Find the correct relation between ‘ $W_{1}$ ’, ‘ $W_{2}$ ’ and ‘ $W_{3}$ ’

A $W_{1} < W_{3} < W_{2}$
B $W_{1} < W_{2} < W_{3}$
C $W_{1} = W_{2} = W_{3}$
D $W_{1} > W_{3} > W_{2}$

Verified Solution

Answer & Solution

Correct Answer

(C) $W_{1} = W_{2} = W_{3}$

Step-by-step Solution

Detailed explanation

∵

Gravitation field in conservative in nature.

∴

Work done will not depend on path

∴ W_{1} = W_{2} = W_{3}

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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If W1,W2 and W3 represent the work done in moving a particle from A to B along three different paths 1,2 and 3 (as shown in figure) in the gravitational field of the point mass ‘ m ’. Find the correct relation between ‘ W1 ’, ‘ W2 ’ and ‘ W3 ’

Step-by-step Solution

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 $3$ (as shown in figure) in the gravitational field of the point mass ‘ $m$ ’. Find the correct relation between ‘ $W_{1}$ ’, ‘ $W_{2}$ ’ and ‘ $W_{3}$ ’