consider a heavenly body which has a mass twice that of the Earth and the radius thrice that of the earth what will be the weight of a body on on this heavenly body if its weight on the earth is 450 Newton
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>(e) denotes earth and (p) denotes the other planet
>m- mass of the body, G- gravitational constant, r- radius of earth, R- radius of planet.
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On earth:
Weight, F(e) = GmM(e) / r^2 -equation 1
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On other planet:
Weight, F(p) = GmM(p) / R^2
(Given: M(p) = 2M(e), R=3r)
implies: F(p) = 2 GmM(e) / [3r]^2 -equation 2
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From dividing equation 2 with equation 1:
F(p) / F(e) = 2 / 9
F(p) = [2/9]*F(e) = [2/9]*450 = 100N
Weight of body on the heavenly body = 100N
>m- mass of the body, G- gravitational constant, r- radius of earth, R- radius of planet.
____________________________________________________________
On earth:
Weight, F(e) = GmM(e) / r^2 -equation 1
____________________________________________________________
On other planet:
Weight, F(p) = GmM(p) / R^2
(Given: M(p) = 2M(e), R=3r)
implies: F(p) = 2 GmM(e) / [3r]^2 -equation 2
____________________________________________________________
From dividing equation 2 with equation 1:
F(p) / F(e) = 2 / 9
F(p) = [2/9]*F(e) = [2/9]*450 = 100N
Weight of body on the heavenly body = 100N
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