Question 245: Gravitation

Question

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

Accepted Answer

$${V_{es}} = \sqrt {{{2GM} \over R}} $$
$${V_{es}}\sqrt R $$ = const
$$ 	herefore $$ $${V_{es}}.\sqrt R  = 10{V_{es}}\sqrt {R'} $$
$$ \Rightarrow $$ $$R' = {R \over {100}}$$ = 64 km

Gravitation

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

Integer / Numeric Answer Type