A rocket is launched straight up from the surface of the earth. When its altitude is one fourth of the radius of the earth, its fuel runs out and therefore it coasts. The minimum velocity which the rocket must have when it starts to coast if it is to escape from the gravitational pull of the earth is [escape velocity on surface of earth is $11.2 k m / s$ ]

Question

A rocket is launched straight up from the surface of the earth. When its altitude is one fourth of the radius of the earth, its fuel runs out and therefore it coasts. The minimum velocity which the rocket must have when it starts to coast if it is to escape from the gravitational pull of the earth is [escape velocity on surface of earth is

11.2 k m / s

]

Toppr Admin · Accepted Answer

R-x2032-R4-x2234-Vscape-x221A-2GMR-x2032-x221A-2GMR-4-x221A-8GMR-x221A-8-xD7-11-2-x2248-10kms

R′=R4∴Vscape=√2GMR′=√2GMR/4=√8GMR=√8×11.2≈10kms

$R' = \frac{R}{4}$
$∴ V_{s c a p e} = \sqrt{\frac{2 G M}{R'}} = \sqrt{\frac{2 G M}{R / 4}} = \sqrt{8 \frac{G M}{R}} = \sqrt{8 \times 11.2} \approx 10 \frac{k m}{s}$