n a region of only gravitational field of mass 'M' a particle is shifted from A to B via three different paths in the figure. The work done in different paths are W₁, W₂, W₃ respectively then (a) W₁ = W₂ = W₃ (b) W₁ > W₂ > W₃ (c) W₁ = W₂ > W₃ (d) W₁ < W₂ < W₃
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Explanation:
The gravitational field is a conservative field i.e. work done by gravitational field to displace a body is independent of its path. In other words, work done is determined by difference in potential energy at initial and final positions of body.
Therefore, W=P
f
−P
i
.(P
f
=final potential energy, P
i
= Initial potential energy )
So, W
1
=P
B
−P
A
and similarly
W
2
=P
B
−P
A
W
3
=P
B
−P
A
Thus W
1
=W
2
=W
3
thus W1 =W2= W3
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