The radius of a Planet A is half the radius of planet B. If the mass of A is Ma, what must be the mass of B so that the value of g on b is half that of its value on A ?
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heya frnd
According to law of Gravitation:
F = GmM/(R^2)
F/m = g = GM/(R^2)
Ra = Rb/2 and ga = 2*gb
Taking the ratio of both the g's;
ga/gb = (Ma/Mb)/[(Ra/Rb)^2]
2 = (Ma/Mb)/[(1/2)^2]
(Ma/Mb)= 2*(1/4)
(Ma/Mb) = 1/2
Therefore, mass of planet B should be two times the mass of planet A to have an acceleration due to gravity half of that of planet
According to law of Gravitation:
F = GmM/(R^2)
F/m = g = GM/(R^2)
Ra = Rb/2 and ga = 2*gb
Taking the ratio of both the g's;
ga/gb = (Ma/Mb)/[(Ra/Rb)^2]
2 = (Ma/Mb)/[(1/2)^2]
(Ma/Mb)= 2*(1/4)
(Ma/Mb) = 1/2
Therefore, mass of planet B should be two times the mass of planet A to have an acceleration due to gravity half of that of planet
Answered by
1
let the g for planet A and B be g1 and g2 respectively.
let the radius of planet A and B be R1 and R2 respectively.
let mass of planet A and B be Ma and Mb respectively.
according to question,
R1 = 1/2 x R2 ⇒ R2 = 2 x R1
g2 = 1/2 g1
as , we know that
g = GM/R²
g1 = G x Ma/ R1² eq.1 ; g2 = G x Mb/R2² eq. 2
Dividing eq. 1 by 2.
g1/g2 = (Ma x R2²) / (R1² x Mb)
2 = Ma x 4R1² / R1² x Mb
Mb = 2 x Ma
hence , mass of planet B should be twice the mass of planet A
plzzz mark brainliest
let the radius of planet A and B be R1 and R2 respectively.
let mass of planet A and B be Ma and Mb respectively.
according to question,
R1 = 1/2 x R2 ⇒ R2 = 2 x R1
g2 = 1/2 g1
as , we know that
g = GM/R²
g1 = G x Ma/ R1² eq.1 ; g2 = G x Mb/R2² eq. 2
Dividing eq. 1 by 2.
g1/g2 = (Ma x R2²) / (R1² x Mb)
2 = Ma x 4R1² / R1² x Mb
Mb = 2 x Ma
hence , mass of planet B should be twice the mass of planet A
plzzz mark brainliest
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