Question

if the diameter of earth is increases 4 times then the critical velocity becomes??
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Answer 1

Escape velocity is given by

$\sf v = \sqrt{\frac{2GM}{R}}$

Given that diameter is increased 4 times → means that radius is increased 4 times

Considering that mass remains constant, new escape velocity v' will be

$\sf v' = \sqrt{\frac{2GM}{4R}}$

Which gives

$\sf v' = \sqrt{\frac{GM}{2R}}$

Taking ratio

v/v' = 2

That is, the new critical velocity becomes half the previous escape velocity