Question

define escape velocity and derive the mathematical expression

Answer 1

escape velocity is the minimum velocity with which a body must be projected vertically upwards in order that it may just escape the gravitational field of the earth. Expression - consider the earth to be a sphere of mass M and radius R with centre O. Suppose a body of mass m lies at point p at distance x from its centre. F=GMm upon x square. The small work done in moving the body through small distance PQ=dx against the gravitational force dW=Fdx = GMm upon x square dx next line W= integration dw= integration from infinity to R GMm upon x square dx next line = GMm integration from infinity to R x raise to the power -2 dx = GMm(-1 upon x) upper limit infinity and lower infinity R and in next line =GMm(-1/ infinity + 1/R)= GMm upon R and in next line therefore 1/2 mve square = GMm upon R or be square =2GM/R and in next line ve =under root 2GM/R or ve = under root gR here ve means escape velocity please draw its diagram yourself , here are some hints to draw the diagram first you draw the diagram of earth as a sphere and let centre O and radius R (and I request you please mark it as a brainiest )

Answer 2

Explanation:

Escape velocity: -The minimum speed with which a body must be projected. in order that it will escape from the earth gravitational filed is called as. escape velocity. Expression of it:-consider a body of mass m on the surface of earth. whose mass and radius are respectively represented by M and R.