AIIMS2019Physics-Gravitation

AIIMS 2019 Physics Gravitational Field MCQ Question

Type: MCQ-numerical-Medium-Class 11

Find the gravitational field at a distance of 2000 km from centre of earth. (Given Rₑₐᵣₜₕ = 6400 km, r = 2000 km, Mₑₐᵣₜₕ = 6 × 10²⁴ kg);

A

1.53 m/s²

B

7.12 m/s²

C

3.06 m/s²

D

1.8 m/s²

Correct Answer

Option C

Detailed Explanation

To find the gravitational field gg at a distance of 2000 km from the center of the Earth, we use the formula g=GMr2g = \frac{GM}{r^2}, where GG is the gravitational constant (6.67×1011N m2/kg26.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2), MM is the mass of the Earth (6×1024kg6 \times 10^{24} \, \text{kg}), and rr is the distance from the center of the Earth (2000 km or 2×106m2 \times 10^6 \, \text{m}). Calculating this gives g3.06m/s2g \approx 3.06 \, \text{m/s}^2, confirming option C as correct.

Options A, B, and D are incorrect as they do not match the calculated value; they may arise from miscalculations or incorrect assumptions about the distance or mass used in the gravitational field formula.

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