Question

the escape velocity of a body on earth is 11.2 km/s .. if earths mass increases twice and radius of earth becomes half.. then what will be its new escape velocity

Answer 1

Escape velocity, ve= (2gR)^1/2………………..(1).

R is radius of the earth.

ve'=(2g'R')^1/2…………………..(2)

g'= G(2M)/(R/2)^2=(GM/R^2)(8)=8 g.

R'=R/2.

Therefore , ve'= (2*8g*R/2)^1/2= (2 gR*16)^1/2=4 ve.