Question

What is Acceleration due to Gravity? Explain formula of relation between g & G ang
find the value of g.​

Answer 1

$\red{\mid{\underline{\overline{\textbf{Answer}}}\mid}}$

In universe, there is a basic law of physics that helps to understand different phenomena like collision, attraction and many more. This basic law states that mass is an inherent property of matter, weight of a body can change but mass of it can't. This law says that a more massive body attracts a body which have less mass than it. Universal law of gravitation also helps in understanding with what force they attract each other.

Since a living organism or any object is less in mass than the planet on which it lives. Therefore every planet attracts the object in it.

The force by which a planet attracts the object is called gravity. Acceleration due to gravity (g) is the acceleration of a body which is in influence of gravity of a planet. It is represented by small g (g).

Whereas G - The universal gravitational constant is only a physical quantity that is involved in calculating the force of attraction between bodies.

There is no relation between acceleration due to gravity and universal gravitational constant.

This is so because, the value of universal gravitational constant as name suggest is constant at any place in universe. But the acceleration due to gravity is vastly different on different celestial bodies.

Value of acceleration due to gravity of earth applied on an object is the ratio of product of its mass and universal gravitational constant to the square of its radius or distance from surface of earth. It can be represented by the expression :

$\maltese \: g = \frac{GM}{ {r}^{2} }$

______________________________________

BY SCIVIBHANSHU

THANK YOU

STAY CURIOUS

Answer 2

(i) Whenever an object is in free fall, a uniform acceleration is observed in it. This acceleration is due to the gravitational force acting on it. This acceleration is known as ‘acceleration due to gravity’. It is denoted by ‘g’.

(ii) We know,

F = mg (F here is Weight – a force) ...[1]

Also,

F = GMm/R² ...[2]

From [1] and [2],

mg = GMm/R²

⇒g = GM/R² (in usual terms).

(iii) Now we have,

G = 6.7 × 10^-11 N-m²/kg²

M (mass of Earth) = 6 × 10²⁴ kg

R (radius of Earth) = 6.4 × 10⁶ m

∴ g = (6.7 × 10-¹¹ N m²/kg²)(6 × 10²⁴ kg)/(6.4 × 10⁶ m)²

⇒ g = (6.7 × 6)/(6.4)² × 10-¹¹+²⁴-¹² m/s²

⇒ g = 0.9814 × 10¹ m/s²

⇒ g = 9.814 m/s².