The escape velocity of a body on the surfa

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The escape velocity of a body on the surface of the earth is $11.2 \,km/s$. If the earth's mass increases to twice its present value and the radius of the earth becomes half, the escape velocity would become ......... $km/s$

A

$5.6$

B

$11.2$

C

$22.4$

D

$44.8$

The escape velocity of a body on the surface of the earth is $11.2 \,km/s$. If the earth's mass increases to twice its present value and the radius of the earth becomes half, the escape velocity would become ......... $km/s$

${v_e} = \sqrt {\frac{{2GM}}{R}} $ 

${v_e} \propto \sqrt {\frac{M}{R}} $

If $M$ becomes double and $R$ becomes half then escape velocity becomes two times.