Question

What is escape velocity ?Obtain an expression for the expression for the escape velocity on earth?

Answer 1

the main velocity with which body has to projected vertically upward ,so that it escape from gravitational pull of earth is known escape velocity

let us consider the body of mass 'm' lying at a distance of 'x' from the center of the earth having mass 'M' .The gravitational pull exerted by the earth such that its work done will be gravitational potential energy.Due to conservation of energy this work done will be same as K.E having velocity

'V' with which the body will escape the earth surface

(1/2) mv^2=(GMm)/R

v^2=(2GM)/R.......(1)

since

g=(GM)R^2

g*R^2=GM

from (1)

GM=(v^2*R)/2

g*R^2=(v^2*R)/2

v=√(2gr)

thus g=9.8m/s   R=6400km

then v=11.2 km/s

Answer 2

the main velocity with which body has to projected vertically upward ,so that it escape from gravitational pull of earth is known escape velocity

let us consider the body of mass 'm' lying at a distance of 'x' from the center of the earth having mass 'M' .The gravitational pull exerted by the earth such that its work done will be gravitational potential energy.Due to conservation of energy this work done will be same as K.E having velocity

'V' with which the body will escape the earth surface

(1/2) mv^2=(GMm)/R

v^2=(2GM)/R.......(1)

since

g=(GM)R^2

g*R^2=GM

from (1)

GM=(v^2*R)/2

g*R^2=(v^2*R)/2

v=√(2gr)

thus g=9.8m/s   R=6400km

then v=11.2 km/s