The weight of an object at a certain height above Earth's surface equa…

Question

The weight of an object at a certain height above Earth's surface equals its weight at depth d = R/2 below the surface. The corresponding height h is approximately

Accepted Answer

C. {'text': '(√2 − 1) R', 'label': 'C'}

1. g at depth d: g_d = g × (1 − d/R). For d = R/2, g_d = g/2.
2. g at height h: g_h = g × R² / (R + h)². Set g_h = g/2.
3. R² / (R + h)² = 1/2 → (R + h)² = 2 R² → R + h = R√2 → h = R(√2 − 1).
4. h ≈ 0.414 R.
_Source: NCERT Class 11 Physics, Ch 7 "Gravitation", §7.4_

Answer

{'text': 'R/2', 'label': 'A'}

Answer

{'text': "R (Earth's radius above surface)", 'label': 'B'}

Answer

{'text': '2R', 'label': 'D'}