Question

Does gravity have a constant acceleration?

Answer 1

Hint: Gravity is the force of gravitation due to Earth. The gravitational force depends on the masses of the Earth and the body close to the Earth and distance from the centre of the Earth. According to Newton’s second law force is given as the product of mass and acceleration. Using both equations, we can determine the acceleration due to gravity.

Complete answer:
Gravity is the gravitational force of attraction of the Earth on all bodies on its surface or close to its surface. The gravitational force of attraction is given by-
$F=\dfrac{GMm}{{{r}^{2}}}$ - (1)
Here, $F$ is the gravitational force
$G$ is the gravitational constant
$M$ is the mass of Earth
$m$ is the mass of body n the surface or close to the surface of the Earth
$r$ is the distance from the centre of the Earth
We know that, According to Newton’s second law of motion,
$F=ma$ - (2)
Here, $a$ is the acceleration of the body
Equating eq (1) and eq (2), we get,
$\begin{align}
  & \dfrac{GMm}{{{r}^{2}}}=ma \\
 & \Rightarrow a=\dfrac{GM}{{{r}^{2}}} \\
\end{align}$
Since the object is assumed to be close to the earth’s surface, $r=R$, $R$ is the radius of earth. Therefore,
$a=\dfrac{GM}{{{R}^{2}}}$
From the equation given above, as the acceleration depends on all constant quantities, it is also a constant and is denoted by $g$ called acceleration due to gravity and its value is $9.8m{{s}^{-2}}$.
Therefore, the acceleration due to gravity is constant and its value is $9.8m{{s}^{-2}}$.

Note:
Gravitational constant is the constant of proportionality in the coulomb’s force given by Coulomb’s law. The Earth’s gravitational force always acts towards the centre of the Earth. In order to escape Earth’s gravitational force, a body will have to travel with velocity equal to escape velocity.