Test: Gravitation - 2 - UPSC MCQ

B is the correct option.If a rock is brought from the surface of the moon to the earth, its weight will change but not its mass. Mass is an invariant physical quantity whereas weight of a body (w = mg) is variable as the value of acceleration due to gravity (g) changes

A body weighs more at the poles than at the equator, because the earth is not a perfect square, but it is flattened at the poles. The distance between the equator and the center of the earth is less than at the poles; therefore the force of gravitation is more at the poles than at the equator; and so it weighs more at the poles than equator. 
Hence, the weight of a body at the poles will be greater than at the equator.

A satellite experiences a continuous gravitational pull, making it a freely falling object. Despite moving at a consistent speed, the gravitational force, directed towards the Earth's center, serves as the essential centripetal force, ensuring the satellite remains in a circular orbit.

The SI unit of acceleration due to gravity, often denoted as "g," is m/s² (meters per second squared). This can be explained as follows:
- Definition of acceleration due to gravity: The acceleration due to gravity is the acceleration experienced by an object in free fall under the influence of gravity alone. On the surface of the Earth, this is approximately 9.8 m/s².
- Units of acceleration: Acceleration is defined as the rate of change of velocity with respect to time. Its SI unit is m/s², which means meters per second squared.
- Interpretation of the unit: The unit m/s² can be understood as the change in velocity (in meters per second) per unit of time (in seconds). In the case of acceleration due to gravity, it represents the increase in velocity per second due to the gravitational force acting on an object.
Therefore, the correct answer is C: m/s².

In SI units, G has the value 6.67 × 10-11 Newtons kg-2 m2. The direction of the force is in a straight line between the two bodies and is attractive. Thus, an apple falls from a tree because it feels the gravitational force of the Earth and is therefore subject to “gravity”.

So all objects, regardless of size or shape or weight, free fall with the same acceleration. In a vacuum, a beach ball falls at the same rate as an airliner. ... The remarkable observation that all free falling objects fall with the same acceleration was first proposed by Galileo Galilei nearly 400 years ago.

At the center gravity is 0 ,gravity decreases as we go down into the earth ,also it decreases as we go above the surface of earth.
So weight w = mg is maximum on the surface because at surface the value of g is maximum.

The Gravitational force between two objects is inversely proportional to the square of distance between them.
So, if the distance between two objects is doubled, then the gravitational force becomes 1 / 2x2.
 That is ¼.

The correct answer is C as body falls freely towards the earth with uniform acceleration (g).

The correct option is B.
Mass of the body is universally the same. It is not affected by acceleration due to gravity and thus is the same everywhere. Hence, mass of body will be same i.e. M at both earth surface & moon surface.

Weight is a fundamental concept in physics that refers to the force exerted on an object due to gravity. Here is a detailed explanation of the given statement:

Weight:

Weight is the force experienced by an object due to the gravitational pull of the Earth or any other celestial body. It is a vector quantity because it has both magnitude and direction. The direction of the weight vector is always towards the center of the celestial body.

Explanation of the given options:

-

A: Is a vector quantity:

- Weight is a vector quantity because it has both magnitude and direction. The magnitude of weight is equal to the product of the mass of the object and the acceleration due to gravity. The direction of weight is always towards the center of the celestial body.
-

B: Of a body in interplanetary space is maximum:

- Weight is directly proportional to the mass of the object. In interplanetary space, where the gravitational field is weak or negligible, the weight of a body would be much less compared to its weight on Earth. Therefore, the weight of a body in interplanetary space is not maximum.
-

C: Increases when the bodies go up:

- As bodies go up in the Earth's atmosphere, they move farther away from the center of the Earth. The distance between the body and the center of the Earth increases, which leads to a decrease in the acceleration due to gravity. Consequently, the weight of the body decreases as it goes up, rather than increasing.
-

D: None of these:

- The correct answer is not "D: None of these" because option A, which states that weight is a vector quantity, is correct.

The value of g near the earth's surface is 9.8 m/s^2.
Explanation:
The acceleration due to gravity, denoted by the symbol g, is a measure of the gravitational force acting on an object. It is defined as the rate of change of velocity per unit of time. Near the Earth's surface, the value of g is approximately constant.
Here is a detailed explanation of why the value of g near the Earth's surface is 9.8 m/s^2:
1. Definition of g: The acceleration due to gravity, g, is the force per unit mass acting on an object in the gravitational field. It is the acceleration experienced by a freely falling object under the sole influence of gravity.
2. Newton's law of universal gravitation: Newton's law states that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. In the case of an object near the Earth's surface, the Earth's mass and the object's mass are the main factors influencing the force of gravity.
3. Gravitational field strength: The gravitational field strength, represented by g, is the force per unit mass acting on an object in a gravitational field. It is defined as the gravitational force experienced by a unit mass placed in the field. Near the Earth's surface, the value of g is approximately constant.
4. Value of g near the Earth's surface: The value of g near the Earth's surface is approximately 9.8 m/s^2. This means that for every kilogram of mass, the force of gravity is approximately 9.8 newtons. This value may vary slightly depending on the location and altitude, but it is a good approximation for most practical purposes.
Therefore, the correct answer is option C: 9.8 m/s^2.

A geostationary satellite revolves around the earth with the same angular velocity and in the same sense as done by the earth about its own axis, i.e. west-east direction. A polar satellite revolves around the earth's pole in north-south direction.

Explanation:
The force of gravitation between two bodies is determined by the following factors:
1. Their separation:
The force of gravitation between two bodies is inversely proportional to the square of the distance between them. As the separation between the bodies increases, the gravitational force decreases. Similarly, as the separation decreases, the gravitational force increases.
2. Gravitational constant:
The force of gravitation also depends on the gravitational constant. The gravitational constant, denoted by G, is a fundamental constant in physics that determines the strength of the gravitational force. It is a universal constant and has the same value throughout the universe.
3. Product of their masses:
The force of gravitation is directly proportional to the product of the masses of the two bodies. If the masses of the bodies increase, the gravitational force between them increases. Similarly, if the masses decrease, the gravitational force decreases.
Therefore, the force of gravitation between two bodies depends on their separation, the gravitational constant, and the product of their masses. All of these factors contribute to the overall strength of the gravitational force.
Answer: D. All of these.

Explanation:


When an object is thrown up, the force of gravity acts on it. The force of gravity is always directed towards the center of the Earth. Therefore, as the object moves upwards, the force of gravity acts in the opposite direction of the motion. It pulls the object downwards, trying to bring it back to the surface of the Earth.


Key Points:
- The force of gravity acts in the opposite direction of the motion when an object is thrown up.
- It pulls the object downwards, trying to bring it back to the surface of the Earth.
- The force of gravity remains constant as the body moves up.
- It does not increase as the body moves up.


So, the correct answer is B: Acts in the opposite direction of the motion.

The correct answer is A as The force of gravitation exists Everywhere in the universe

1 kg-wt and express it in newton. 1 kilogram weight is that gravitational force which acts on a body of mass 1 kg. This means that the weight of 1 kgmass is 9.8 N.
Hence the answer is option (a)

Density,
ρ = M / V = 11040 / 12
= 920 kg/m³

Explanation:
The value of the gravitational constant (G) is a fundamental constant in physics that determines the strength of the gravitational force between two objects. It is a universal constant and is the same for all objects in the universe. Therefore, the value of G does not depend on any specific characteristics of the interacting bodies, such as their nature, size, or mass. This can be explained as follows:
Nature of the interacting bodies:
- The gravitational constant is independent of the nature of the interacting bodies. It does not matter whether the bodies are made of different materials or have different chemical compositions. The value of G remains the same for all objects.
Size of the interacting bodies:
- The value of G is not influenced by the size of the interacting bodies. Whether the bodies are large or small, the gravitational constant remains constant.
Mass of the interacting bodies:
- The value of G is also not affected by the mass of the interacting bodies. Whether the bodies have a large or small mass, the gravitational constant remains unchanged.
All of these:
- Since the value of G is independent of the nature, size, and mass of the interacting bodies, it can be concluded that the answer is option D: All of these. None of these factors have any influence on the value of G.
Therefore, the value of the gravitational constant G does not depend on the nature of the interacting bodies, the size of the interacting bodies, or the mass of the interacting bodies. It remains constant regardless of these factors.

F = GMm / r²
= 6.67×10-¹¹ × (1.99×10³⁰) × (1.9×10²⁷) / (7.8×10¹¹)² 
= 4.14×10²³ N
Now let its speed of jupiter be v, then
F = mv² / R
⇒ v =√(FR / m)
=√{(7.8×10¹¹)×(4.10×10²³) / (1.9×10²⁷)}
= 1.304×10⁴ m/sec

Explanation:
The acceleration due to gravity is the force of gravity acting on an object. It is the rate at which an object falls towards the Earth. Here, we are given a statement and we need to determine which option is correct.
Options:
A: The statement says that the acceleration due to gravity has the same value everywhere in space. This is incorrect because the acceleration due to gravity can vary depending on the distance from massive objects.
B: The statement says that the acceleration due to gravity has the same value everywhere on the Earth. This is also incorrect because the acceleration due to gravity can vary depending on the altitude and the shape of the Earth.
C: The statement says that the acceleration due to gravity varies with the latitude on the Earth. This is correct because the Earth is not a perfect sphere, but rather an oblate spheroid. The acceleration due to gravity is slightly greater at the poles and slightly smaller at the equator.
D: The statement says that the acceleration due to gravity is greater on the moon due to its smaller diameter. This is incorrect because the acceleration due to gravity on the moon is about one-sixth of that on Earth due to the moon's smaller mass.
Therefore, the correct answer is C: the acceleration due to gravity varies with the latitude on the Earth.

Weight is nothing but the force of attraction exerted by the earth on a body.
Now since the SI unit of force is Newton and the weight is also a force, this means that the SI or weight is Newton as well.

Gravitational force which acts on 1 kg is 9.8 N.

Weight is
Weight is a measurement of the force exerted on an object due to gravity. It is different from mass, which is a measure of the amount of matter in an object.
Weight can be measured using various methods:
- Measured by a spring balance: A spring balance is a device that uses the stretching or compression of a spring to measure the force exerted on an object. The force exerted by an object due to gravity can be measured using a spring balance, which is calibrated to measure weight in units such as Newtons or pounds.
- Measured by a beam balance: A beam balance is a device that uses the principle of equilibrium to measure the weight of an object. It consists of a beam supported at a fulcrum, with two pans hanging from either end. The weight of the object can be determined by comparing the balance of the beam when the object is placed on one pan with the balance when standard weights are placed on the other pan.
- Measured in kg: Weight is commonly expressed in units of mass, such as kilograms or pounds. However, it is important to note that weight is not the same as mass. Mass is a scalar quantity that remains constant regardless of the location, while weight depends on the gravitational force acting on the object and can vary based on the strength of the gravitational field.
- A scalar quantity: Weight is a scalar quantity, meaning it has magnitude but no direction. It is different from a vector quantity, which has both magnitude and direction. Weight only indicates the amount of force exerted on an object due to gravity, without specifying the direction of the force.

In conclusion, Weight is a vector quantity It is measured using a spring balance its Si unit is newton (N).