Whenever objects fall towards the earth under this force alone, we say that the objects are in free fall. Is there any Whenever objects fall towards the earth under this force alone, we say that the objects are in free fall. Is there any But due to the earth’s attraction, there will be a change in the magnitude of the velocity. Any change in velocity involves acceleration. Whenever an object falls towards the earth, an acceleration is involved. This acceleration is due to the earth’s gravitational force. Therefore, this acceleration is called the acceleration due to the gravitational force of the earth (or acceleration due to gravity). It is denoted by g. The unit of g is the same as that of acceleration, that is, ms–2.
F = ma (`because`a = g) ...(1)
F = mg ...(2)
and `"F" = "G"("Mm")/"d"^2` (`therefore` Universal law of gravitation) ...(3)
From (ii) and (iii)
`therefore` `"mg" = "G"("Mm")/"d"^2`
`therefore` `"g" = "GM"/"d"^2`
M = Mass of the earth.
d = Distance between the object and the earth.
G = Gravitational constant
If the object is placed on the earth then d = R (radius of the earth)
`therefore` `"g" = "GM"/"R"^2`
Earth is not a sphere it is flattened at poles.
Hence Rp - Radius at pole and Re - Radius at equator Re > Rp
`"g" ∝ 1/"R"`
`therefore` The value of 'g' is more at poles = (9.9 m/s2) and less at the equator = (9.8 m/s2)
Shaalaa.com | Acceleration due to gravity
A force acts for 10 s on a stationary body of mass 100 kg, after which the force ceases to act. The body moves through a distance of 100 m in the next 5 s. Calculate : The acceleration produced by the force
Figure shows the velocity-time graph of a particle of mass 100 g moving in a straight line. Calculate the force acting on the particle.
(Hint : Acceleration = Slope of the v-t graph)
A force causes an acceleration of 10 m s-2 in a body of mass 500 g. What acceleration will be caused by the same force in a body of mass 5 kg?
A force acts for 0.1 s on a body of mass 2.0 kg initially at rest. The force is then withdrawn and the body moves with a velocity of 2 m s-1. Find the magnitude of the force.