Question

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

Answer 1

64 km

solution::

Escape velocity =\(\sqrt{2GM\over R}\) 

we know mass remain unchanged 

\(V_e' \over V_e\) =\(\sqrt{R_e\over R_e'}\)  

\({{10V\over e}\over {V\over e}} ={\sqrt{6400\over R_e'}}\) 

\(R_e'=64 km\)