Form 4 Gravitation problem

Ian Langley

2011-06-13 4:17 am

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a) Show that the difference between the mass of the granite rock and mass of an equivalent volume of the surrounding material is 5.0X10^10 kg.

b) The universal gravitational constant G = 6.7X10^-11 N m^2 kg^-2. Calculate the difference between the gravitation field strength at B and that at point A on the Earth's surface that is a long way from the granite rock.

回答 (1)

天同

2011-06-13 5:51 am

✔ 最佳答案

(a) Volume of granite rock = (4/3).pi.(200)^2 m^3 = 3.351 x 10^7 m^3
Hence difference in mass
= (3700 x 3.351 x 10^7 - 2200 x 3.351 x 10^7) kg = 5 x 10^10 kg

(b) Graviational field strength g' at B
g' = GM'/R^2 + K
where M' is the mass of the granite rock
R is the distance of the centre of the granite rock from the surface (= 400 m)
K is a constant representing the contribution to the field strength from the rest of the surrounding materials

Gravitational field strength g at A
g = GM/R^2 + K
where M is the mass of an equivalent volume of the surrounding material

Hence, g' - g = GM'/R^2 - GM/R^2
i.e. g' - g = (G/R^2).(M' - M) = [(6.7x10^-11)/400^2] x (5 x 10^10) N/kg
g' - g = 2.09 x 10^-5 N/kg

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