HOTS Questions: Gravitation - Class 9 MCQ

Universal gravitational constant is represented by ‘G’. S.I. unit of universal gravitational constant is Nm²/Kg². As G = Fxr²/Mm.

Given The mass of the body on moon is 40 kg , what is the weight on the earth ?

Now we have mass of body on moon m = 40 kg.

We know that weight on earth is given by mass x gravitational force

 So w = m x g

       w = 40 x 9.8 m/s²

      w = 392 N

So weight on the earth is 392 N

When a body is thrown upwards, the direction of ‘g ‘ is negative that slows down the speed of body. When the body is falling downward, the direction of ‘g’ is downward direction.

The correct option is B.
 Objects of different masses falling freely near the surface of the earth would have the same velocities at any instant because they will have the same acceleration due to gravity.

The force acting on two bodies is inversely proportional to square of the distance between them. Therefore,Fα 1/r².

Polar radius is 6357 km and equatorial radius is 6378 km. The shape of earth is not perfectly spherical. Poles are slightly closer to centre of earth. Weight of body at particular place is product of mass and acceleration due to gravity. So, weight and mass of body at particular position never be equal.

Initial velocity ,u= 20 m/s. final velocity = o , g = 10ms⁻² . V = u + gt, 0 = 20+(−10)×t20+(−10)×t, t = 20/10 = 2s. time taken to fall in downward direction = 2s. hence total time taken = 2s +2s = 4s.

Explanation:
When a stone falls towards the earth, both the stone and the earth attract each other due to the force of gravity. This is known as the law of universal gravitation. Here's a detailed explanation:
Law of Universal Gravitation:
- The law of universal gravitation states that every object in the universe attracts every other object 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.
- This means that both the stone and the earth exert a gravitational force on each other.
Stone's attraction towards Earth:
- The stone is attracted towards the earth due to its gravitational force.
- The earth has a much larger mass than the stone, so the force of attraction is more significant on the stone.
- This force causes the stone to accelerate towards the earth, resulting in its fall.
Earth's attraction towards Stone:
- According to Newton's third law of motion, for every action, there is an equal and opposite reaction.
- As the stone attracts the earth towards itself, the earth also attracts the stone towards it with an equal force.
- However, due to the earth's large mass, the acceleration caused by this force is negligible and is not noticeable.
Conclusion:
- Both the stone and the earth attract each other due to the force of gravity.
- The stone falls towards the earth as a result of this attraction.
- Therefore, option (C) is correct: Both the stone and the earth attract each other.

Correct Answer :- b

Explanation:- Force of gravitation is equal to product of masses divided by square of the distance between them. So, the force of gravitation between two bodies will be the same irrespective of their place. 

So, the ratio will be 1:1.

Gravitational force is a weak force. This force exists between each and every object but cannot be felt until the mass of the bodies are not extremely high like planets.

(c) They have the same velocities at any instant

Explanation: Two different masses falling freely near the moon’s surface have the same velocities at any instant

Pressure = force/ area. Here, Force = 200N. Area=5m². So, pressure = 200N/5m 25m² = 40 Pa.

The value of universal gravitational constant (G) is6.67×10⁻¹¹Nm²/Kg²  Which is constant and independent of mass, distance between the bodies and other factors.

Earth and moon attracts each other with equal gravitational force. The mass of a body never becomes 0. Hence both statements are incorrect.

Mass of the body (m) = 100 kg, acceleration due to gravity (g) =9.8 m/s29.8 m/s2. Weight (w) = m×gm×g=100×9.8100×9.8= 980N.

Gravitational force between two bodies F = G Mm/r2G Mm/r2. The value of force exerted on m due to M will be equal to that of M due to m. so, the ratio will be 1;1.

Force of gravitation:
The force of gravitation between two objects is given by the universal law of gravitation, which states that the force is directly proportional to the product of the masses of the two objects and inversely proportional to the square of the distance between them.
Key points:
- The force of gravitation is directly proportional to the product of the masses of two objects. This means that if the mass of one of the objects increases, the force of gravitation will also increase. Similarly, if the mass of both objects increases, the force of gravitation will increase even more.
- The force of gravitation is inversely proportional to the square of the distance between the two objects. This means that as the distance between the objects increases, the force of gravitation decreases. Conversely, as the distance decreases, the force of gravitation increases.
- The force of gravitation acts between all objects in the universe, but its strength decreases rapidly with increasing distance. This is why we usually only notice the force of gravitation between large objects like planets and stars.
- The force of gravitation is a fundamental force of nature and plays a crucial role in shaping the structure and behavior of the universe. It is responsible for keeping planets in orbit around the sun, for the tides on Earth, and for many other phenomena.
Conclusion:
The force of gravitation is directly proportional to the product of the masses of two objects and inversely proportional to the square of the distance between them. Therefore, option A, which states that the force of gravitation is directly proportional to the product of masses of two objects and inversely proportional to the square of distance between two objects, is the correct answer.

Weight:

1. The weight of a body on the earth is the force with which the earth attracts a body.
2. The formula for the weight is 
3. The weight of a body depends on the mass and the acceleration due to gravity.
4. Earth is not a perfect sphere. The radius at the equator is greater than the poles.
5. Acceleration due to gravity is inversely proportional to the square of the radius. So, the value of acceleration due to gravity (g) is greatest at the poles.
6. Weight depends on acceleration due to gravity and acceleration due to gravity is greatest at the poles. So, the weight of a body is greatest in the region of the pole.
7. The bears found in the polar region are polar bears which are white in color

Hence, the weight of an object is greatest in the region of the pole and the bears found in the polar regions are white in color.

The upward force experienced by the body when partially or completely submersed in fluid.

Gravitational force is always attractive in nature irrespective of the distance and mass of bodies. this decreases with distance but cannot be repulsive.

In science, an inverse-square law is any scientific law stating that a specified physical quantity is inversely proportional to the square of the distance from the source of that physical quantity.Since the gravitational field lines go radially inward towards the mass, the density of the field lines would be inversely proportional to the surface over which they are spread over and therefore inversely proportional to r^2. Since force is proportional to the density of field lines, the force is inversely proportional to distance squared.

Application of Earth's Gravitation:
- Holding the atmosphere around our globe: Earth's gravity holds the atmosphere close to the surface of the Earth. Without gravity, the atmosphere would disperse into space.
- Keeping us firmly on the surface of the Earth: Earth's gravity pulls everything towards its center, which keeps us and all objects on the surface of the Earth. It gives us our weight and prevents us from floating away.
- Motion of the moon: Earth's gravity also affects celestial bodies like the moon. The gravitational force between the Earth and the moon keeps the moon in its orbit around the Earth.
- Causing sea tides due to the moon: The gravitational pull of the moon on the Earth's oceans creates the phenomenon of tides. The moon's gravity causes the water to bulge towards the moon, creating high tide, and also causes a bulge on the opposite side of the Earth, creating low tide.
Conclusion:
Earth's gravitation has multiple applications, including holding the atmosphere, keeping us on the surface, influencing the motion of the moon, and creating sea tides.

Acceleration due to gravity (g) on moon is 1/6^th of the acceleration of gravity (g) on earth. So, weight of body of 10N on the surface of moon will be 1/6×10N = 1.67N.

Value of g depends upon mass of the planet and radius, acceleration due to gravity does not change due to air friction. Body moving in upward direction will have gravitational force in downward direction.

Mass is a scalar quantity. It is a measure of the inertia of an object. Mass can be represented by a number only. The SI unit of mass is kg. 

Explanation:
The universal law of gravitation states that the force between two bodies is determined by the following factors:
(i) Force is directly proportional to the product of masses of two bodies:
- This means that as the mass of one body increases, the force of attraction between the two bodies also increases.
- Mathematically, this can be represented as F ∝ m1 * m2, where F is the force and m1 and m2 are the masses of the two bodies.
(ii) Force is inversely proportional to the square of the distance between two bodies:
- This means that as the distance between two bodies increases, the force of attraction between them decreases.
- Mathematically, this can be represented as F ∝ 1/r^2, where F is the force and r is the distance between the two bodies.
Therefore, the correct answer is C: (i) and (ii)