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JEE Main 2023 · 25 Jan · Shift 2

JEE Main 2023 Physics question on Gravitation

A body of mass is taken from earth surface to the height h equal to twice the radius of earth (Re)(R_e), the increase in potential energy will be:

(g=acceleration due to gravity on the surface of Earth)(g = \text{acceleration due to gravity on the surface of Earth})
  1. A.
    3 mgRe3 \, mgR_e
  2. B.
    13mgRe\frac{1}{3} mgR_e
  3. C.
    12mgRe\frac{1}{2} mgR_e
  4. D.
    23mgRe\frac{2}{3} mgR_e
Show answer and solution

Correct option: D

Solution

The gravitational PE at surface is -GMm/Rₑ and at height h = 2Rₑ it is -GMm/(Rₑ + 2Rₑ) = -GMm/3Rₑ.

Increase in PE = (-GMm/3Rₑ) - (-GMm/Rₑ) = GMm/Rₑ · (1 - 1/3) = (2/3)(GMm/Rₑ).

Since g = GM/Rₑ², we have GM/Rₑ = gRₑ, so the increase in PE = (2/3)mgRₑ.

[JEE Main 2023 · 25 Jan · Shift 2]

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