MCQ : Gravitation - 1 - UPSC

With depth, g₁ = g {1− (d)/R}

As depth d goes on increasing, g1 goes on decreasing, it remains maximum at the surface of Earth. The above equation is in the form of a straight line.

With height, g₂ = g (1 − 2h/R) = g − 2gh/R

g₂ ∝ 1/R (Hyperbola)

Acceleration due to gravity goes on decreasing as the h above Earth surface increases.

In SI units, G has the value 6.67 × 10^-11 N kg^-2 m². 

The acceleration due to gravity on the surface of a planet depends on the mass and radius of the planet. The formula for acceleration due to gravity on the surface of a planet is:

g = G * M / R^2

where: g = acceleration due to gravity G = gravitational constant M = mass of the planet R = radius of the planet

Since all the planets are made up of the same material, we can assume that they have the same density. Therefore, the mass of the planets is proportional to their volume, which is proportional to the cube of their radius. So we can write:

M ∝ R^3

Substituting this in the formula for acceleration due to gravity, we get:

g = G * (R^3) / R^2 = G * R

So the acceleration due to gravity is directly proportional to the radius of the planet.

Therefore, the order of the planets in increasing order of acceleration due to gravity on their surface is:

A < B < C < D

Since the radius of planet A is r/2, its acceleration due to gravity is (1/2)Gr. The radius of planet B is r, so its acceleration due to gravity is Gr. The radius of planet C is 2r, so its acceleration due to gravity is 2Gr. The radius of planet D is 4r, so its acceleration due to gravity is 4G*r.

So the correct order is: A, B, C, D.

• Moon is the closest heavenly body to the Earth. The sun is approximately 400 times farther than the Moon. Hence, its Gravitational pull is weaker than the Moon.
• So, the tides are mainly caused by the Gravitational interaction between Moon & Earth.

• An action-reaction pair of forces are always equal and opposite, but two forces that are equal in magnitude and opposite in direction are NOT always an action-reaction pair!
• On the other hand, the reaction force to the normal force pushing up on the book is the force of the book pushing down on the table.

Acceleration due to gravity at the moon is (1/6)^th times of that at the earth.
So, weight on moon, W_m = W_e /6 = 10/6 = 1.67 N 

Given:
Weight on Earth = 60 kg
Gravity on Moon is (1/6)th the gravity on Earth
Hence, weight on Moon will be 60/6=10 kg.

• The weight of an object is the force with which it is attracted towards the earth. The SI unit of weight is the same as that of force, that is, newton (N).
• The weight is a force acting vertically downwards; it has both magnitude and direction.
• w = m*g

The acceleration due to gravity on the surface of the moon is 1/6th of its value on the surface of the earth because they have different mass, density, and radius. Here's a detailed explanation:
1. Mass: The mass of an object determines the strength of its gravitational pull. The moon has much less mass than the Earth, which means it has a weaker gravitational force. The mass of the moon is about 1/6th of the Earth's mass.
2. Density: Density is defined as mass per unit volume. The moon has a lower average density compared to the Earth. This means that the same mass of material takes up more space on the moon compared to the Earth. The lower density contributes to the weaker gravitational force on the moon.
3. Radius: The radius of an object affects the gravitational force it exerts. The moon has a smaller radius than the Earth, which means that the distance between an object on the moon's surface and its center is smaller compared to the Earth. The smaller distance results in a weaker gravitational force on the moon.
4. All of these: The combination of the moon's lower mass, lower density, and smaller radius compared to the Earth leads to a gravitational force on the moon that is only 1/6th of the force on the Earth's surface. Therefore, the correct answer is option D, all of these factors contribute to the difference in acceleration due to gravity between the moon and the Earth.
In summary, the acceleration due to gravity on the moon is 1/6th of its value on the Earth because the moon has a smaller mass, lower density, and smaller radius compared to the Earth.

By Newton's universal law of gravitation, F = Gm₁m₂ / r². Thus, F is inversely proportional to r².