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The escape velocity of a sphere of mass m is given by (G=Universal gravitational constant,M=Mass of the earth and R_(e )=Radius of the earth) |
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Answer» `sqrt((2GMm)/(R_(e ))` Therefore in order to take a body from the earth.s surface to infinity, the work required is `(GMm_(e )m)/(R_(e ))`. Hence it is evident that if we throw a body of mass m with such a velocity that its kinetic energy is `(GM_(e )m)/(R_(e ))`, then it will move outside the gravitational field of earth. Hence, `(1)/(2)mv_(e )^(2)=(GM_(e )m)/(R_(e ))" or ", v_(e )=sqrt((2GM_(e ))/(R_(e )))`. |
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