A body weighs 48 N on the surface of the Earth. The gravitational force experienced by the body due

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Question

A body weighs 48 N on the surface of the Earth. The gravitational force experienced by the body due to the Earth at a height equal to one-third the radius of the Earth from its surface is:

Accepted Answer

Correct Answer: C — 27 NStep-by-step Solution:Given: W = mg = 48 N; h = R/3 (height above surface)Distance from Earth's centre: R + h = R + R/3 = 4R/3Gravitational force at height h:Wh = GMm/(R+h)² = GMm/(4R/3)² = GMm × 9/(16R²)Wsurface = GMm/R²Wh/Wsurface = 9/16Wh = (9/16) × 48 = 9 × 3 = 27 NWhy Option A (36 N) is wrong: Would require the ratio Wh/W = 3/4 — this would correspond to h = R(√(4/3) − 1) ≈ 0.155R, not R/3.Why Option B (16 N) is wrong: Would require ratio = 1/3, corresponding to h = (√3 − 1)R ≈ 0.73R, not R/3.Why Option D (32 N) is wrong: Would require ratio = 2/3. Correct ratio is 9/16 = 0.5625, giving 27 N.Key Concepts from Gravitation (NCERT Class 11, Chapter 8):Gravitational force at height h above Earth's surface: Fh = GMm/(R+h)².Variation with height: gh = g/(1 + h/R)². For h h ≈ g(1 − 2h/R).Weight on surface: W = mg = GMm/R². At height h: Wh = mgh.Ratio: Wh/W = R²/(R+h)² = [R/(R+R/3)]² = [R/(4R/3)]² = (3/4)² = 9/16.

A body weighs 48 N on the surface of the Earth. The gravitational force experienced by the body due to the Earth at a height equal to one-third the radius of the Earth from its surface is:

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A body weighs 48 N on the surface of the Earth. The gravitational force experienced by the body due to the Earth at a height equal to one-third the radius of the Earth from its surface is:

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Frequently Asked Questions