Escape velocity from the Earth's surface (g = 9.8 m s⁻², R = 6.4 × 10⁶ m) is closest to:
A5.6 km s⁻¹
B7.9 km s⁻¹
C11.2 km s⁻¹
D16.0 km s⁻¹
Answer & Solution
Correct answer: C. 11.2 km s⁻¹
1. v_e = √(2 g R).
2. Compute: 2 × 9.8 × 6.4 × 10⁶ = 1.2544 × 10⁸ m² s⁻².
3. v_e = √(1.2544 × 10⁸) ≈ 1.12 × 10⁴ m s⁻¹.
4. Convert: 11.2 km s⁻¹.
5. The distractor 7.9 km s⁻¹ is the orbital speed at the surface — √(gR) ≈ 7.9 km s⁻¹.
_Source: NCERT Class 11 Physics Ch 7 "Gravitation", §7.8 (worked discussion of v_e), p. 136_
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