a small body is initially at a distance r from the centre of the Earth. r is greater than the radius of the earth. if it takes W joule of work to move the body from this position to another position at a distance 2r measured from the centre of the Earth, how many joules would be required to move it from this position to a new position at a new position at a distance of 3rd from the centre of the Earth
Answers
Lets assume that the mass of earth be "M" and mass of small body by "m"
at distance "r" from the center of earth , the initial gravitational potential energy is given as
U₁ = - GMm/r eq-1
Similarly , at distance "2r" from the center of earth , the final gravitational potential energy is given as
U₂ = - GMm/(2r) eq-2
W= work done in moving the body from distance "r" to distance "2r" from the center
Work done is given as
W = U₂ - U₁
W = (- GMm/(2r)) - ( - GMm/r )
W = GMm/(2r)
2W = GMm/r eq-3
Similarly , at distance "3r" from the center of earth , the final gravitational potential energy is given as
U₃ = - GMm/(3r)
W' = work done in moving the body from distance "r" to distance "3r" from the center
work done is given as
W' = U₃ - U₁
W' = (- GMm/(3r)) - (- GMm/r)
W' = (GMm/r) (1 - (1/3))
using eq-3
W' = (2W) (2/3)
W' = (4W/3)