The relation between acceleration due to gravity (g) and universal gravitational constant (G) is given by:

Explore Exams

Games Login / Register

All Exams Test series for 1 year @ ₹349 only

Question

RRB ALP - 2018

Physics

The relation between acceleration due to gravity ($g$) and universal gravitational constant ($G$) is given by:

This question was previously asked in

RRB ALP 2018 CBT 2 Fitter Question Paper (21-Jan-2019) (Shift 3)

Attempt Now

$G = \frac{gM}{R^2}$

$R = \frac{GM}{g}$

$g = \frac{GM}{R^2}$

$M = gGR^2$

The correct answer is

$g = \frac{GM}{R^2}$

The question asks for the relationship between acceleration due to gravity ($g$), the universal gravitational constant ($G$), the mass of the planet ($M$), and its radius ($R$).

Gravity Formula Derivation

We can derive the formula for acceleration due to gravity ($g$) using Newton's Law of Universal Gravitation and Newton's Second Law of Motion.

Newton's Law of Universal Gravitation states that the force ($F$) between two masses $M$ and $m$ separated by a distance $R$ is:
$F = \frac{GMm}{R^2}
Newton's Second Law of Motion states that the force acting on a mass $m$ is:
$F = mg
For an object on the surface of a planet (or other celestial body) of mass $M$ and radius $R$, the gravitational force experienced by the object is responsible for its acceleration $g$. Therefore, we can equate the two expressions for force:
$mg = \frac{GMm}{R^2}
By canceling the mass of the object ($m$) from both sides, we get the relationship for acceleration due to gravity:
$g = \frac{GM}{R^2}

Resulting Gravity Equation

The derived equation shows the direct relationship between acceleration due to gravity ($g$) and the universal gravitational constant ($G$), the mass ($M$) of the central body, and its radius ($R$). This matches Option 3.

Was this answer helpful?

Important Questions from Universal law of gravitation

Which of the following laws says that "Every object in the universe attracts every other object with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them?"
Physics
View Answer
The force of attraction between two objects of masses 'M' and 'm' which lie at a distance 'd' from each other is directly proportional to the-
Physics
View Answer
The force of attraction (F) between two particles having masses m ₁and m ₂is given by _______. (If r is the distance between them and G is a universal constant)
Physics
View Answer
Three point masses each of mass m are placed at the three corners of an equilateral triangle of side x. Find the resultant force acting on any one particle at the corner.
Physics
View Answer
Imagine a light planet is revolving around a star in a circular orbit of radius R with the period of revolution T . If the gravitational force of attraction between the two is proportional to R^(-5/2) then
Physics
View Answer