Gravitation Test - 3

While calculating the gravity at any point, the distance of point is considered from the centre of the earth. Hence, even if the earth is replaced by a small point sized particle of the same mass, the distance of a point at the present surface of the earth remains the same. Therefore, the gravity will remain the same.

Gravitation attraction of the sun and the moon on the oceans of the earth are responsible for tides.

F = Gm₁m₂/r²,where F = gravitation force between the Sun and Earth, G = universal gravitation constant, m₁ = mass of the Sun, m₂ = mass of Earth and r = distance between the Sun and Earth.

Now, when the distance between the two bodies is doubled, the distance becomes 2r and the force is denoted by F'.

F' = Gm₁m₂/(2r)²
F' = F/4

g = GM/R²
g' = G(2M)/(2R)²
g' = g/2 = (9.8/2) m/s² = 4.9 m/s²

Moreover at the center of the earth, the force of gravity is maximum. So, the rate of fall of gravity going up the earth's surface is double the rate when going down the earth's surface.

The weight of an object in a coal mine is lesser than the weight of that object at sea level. The weight of an object is lesser on the top of a mountain than at sea level.

(i) Escape velocity is √2 times the orbital velocity.
(ii) A body with a velocity equal to the orbital velocity will orbit the planet in a circular path.