A particle is kept at a distance R above the earth’s surface. What is the minimum speed with which it should be projected so that it does not return?(a) [(G*M)/(4*R)]^1/2(b) [(G*M)/(2*R)]^1/2(c) [(G*M)/R] ^1/2(d) [(2*G*M)/R]^1/2The question was asked during an interview.My enquiry is from Gravitation in portion Gravitation of Physics – Class 11

A particle is kept at a distance R above the earth’s surface. What i

1.	A particle is kept at a distance R above the earth’s surface. What is the minimum speed with which it should be projected so that it does not return?(a) [(GM)/(4R)]^1/2(b) [(GM)/(2R)]^1/2(c) [(GM)/R] ^1/2(d) [(2G*M)/R]^1/2The question was asked during an interview.My enquiry is from Gravitation in portion Gravitation of Physics – Class 11
Answer» RIGHT option is (c) [(G*M)/R] ^1/2 For EXPLANATION I would SAY: If the object’s initial velocity is “v”, from the LAW of conservation of energy, we have; (m X v^2)/2 = (G x M x m)/(R+R) v^2 = (2 x G x M)/(2x R) Therefore; v = [(G x M)/R]^1/2.

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