Overview Physics Gravitation Physics Class 11th

The radius in kilometre to which the radius of earth (R = 6400 km) to be compressed so that the escape velocity is increased 10 times is ................

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Answered by

Vishal Baghel | Contributor-Level 10

a month ago

The formula for escape velocity (v_e) is v_e = √ (2GM/R).
According to the question, the new escape velocity (v_e') from a new radius R' is related to the original escape velocity by 10v_e' = v_e.
10 * √ (2GM/R') = √ (2GM/R)
Squaring both sides:
100 * (2GM/R') = (2GM/R)
100/R' = 1/R
R' = R/100

If R is the radius of Earth (6400 km), then:
R' = 6400 km / 100 = 64 km

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