The escape velocity of a body on the earth surface is 11.2 km/s. If the same body is projected upward with velocity 22.4 km/s, the velocity of this body at infinite distance from the centre of the earth will be: (a) 11.2√(2) km/s (b) Zero (c) 11.2 km/s (d) 11.2√(3) km/s

Answer: (d). v∞² = v² - ve² (energy conservation). v = 22.4 = 2ve ⇒ v∞² = 4ve² - ve² = 3ve² v∞ = √(3) ve = 11.2√(3) km/s So the answer is (d) 11.2√(3) km/s.

The escape velocity of a body on the earth surface is 11.2 km/s. If… | NEET 2023

Q38NEET 2023Medium

Escape Velocity

The escape velocity of a body on the earth surface is $11.2\text{ km/s}$ . If the same body is projected upward with velocity $22.4\text{ km/s}$ , the velocity of this body at infinite distance from the centre of the earth will be:

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Answer: (d)

$v_\infty^2 = v^2 - v_e^2$ (energy conservation).
$v = 22.4 = 2v_e \Rightarrow v_\infty^2 = 4v_e^2 - v_e^2 = 3v_e^2$
$v_\infty = \sqrt{3}\,v_e = 11.2\sqrt{3}\text{ km/s}$
So the answer is (d) $11.2\sqrt{3}\text{ km/s}$ .

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