Q.1) State Newton's Law of Gravitation. Derive the equation, F = ${\frac{Gm₁m₂}{r}}$
Ans) Newton's Law of Gravitation:Newton's Law of universal gravitation states that: Every body in the universe attracts every other body with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.
Derivation of Newton's Law of Gravitation:
To understand this Law, we consider two bodies of masses m₁, and m₂. The distance between their centres is r. As shown in the figure.
According to the statement force of attraction between two bodies is directly proportional to the product of their masses. Therefore,
F ∝ m₁m₂ ............ (i)
The gravitational force of attraction is inversely proportional to the square of the distance between the centres of the masses of the bodies. Therefore,
F ∝ ${\frac{1}{r^2}}$ ............ (ii)
Combining equation (i) and equation (ii):
F ∝ ${\frac{m₁m₂}{r^2}}$
F = G${\frac{m₁m₂}{r^2}}$
More Information:
Sir Isaac Newton's was one of the greatest scientists in the world. He made fundamental contributions not only the several branches of Physics (like optics and mechanics) but also to Astronomy and Mathematics. He formulated the laws of motion and the law of universal gravitation.
Q.2) What changes the path of the moon around the earth?
Ans) The pull of gravity changes the path of the Moon around the Earth.
Q.3) What are the characteristics / key points of gravitational force?
Ans)
Characteristics / Key Points of Gravitational Force:
Gravitational force has the following characteristics:
(i) It is always present between every two objects because of their masses.
(ii) It exists everywhere in the universe.
(iii) It forms an action-reaction pair.
(iv) It is Independent of the medium between the objects.
(v) It is directly proportional to the product of the masses of objects.
(vi) It is inversely proportional to the square of the distance between the centres of the objects.
(vii) Hence it follows the “inverse Square Law”.
Q.4) Is Newton’s law of gravitation fan consistent with Newton s third law of motion?
Ans)
Law of Gravitation and Newton's Third Law of Motion:
According to Newton's law of gravitation, every two objects attract each other with equal force but in opposite directions. As shown in the given figure.
From the figure:
m₁ = mass of body A
m₂ = mass of body B
F₁₂ = force with which body A attracts body B
F₂₁ = force with which body B attracts body A
Then according to this law,
F₁₂ = - F₂₁
This shows that the two forces are equal in magnitude but opposite in direction. Now, if F₁₂ is considered as “Action Force” and F₂₁ as “Reaction Force”. Then by using the above equation, it is concluded that “Action Moon equals to reaction but in opposite direction”.
Recall that, above statement is in accordance with Newton's third Law of motion which states that "To every action, there is always an equal and opposite reaction". Hence, Newton’s law of gravitation is consistent with Newton’s third low of motion. For example, according to Newton’s law of universal gravitation, the Earth pulls the Moon with its gravity and the Moon pulls the Earth with its gravity. Therefore they form an action-reaction pair, which is in accordance with Newton's third Law of motion.
Q.5) Define gravitational field. Describe the Earth's gravitational field.
Ans) Gravitational Field:
"Gravitational field is a region in which a mass experiences a force due to gravitational attraction".
Earth's Gravitational Field:
The earth has an attractive gravitational field around it. Any object near the earth experiences this fore which is due to earth's gravity. This field is directed towards the center of the earth.
This field is the strongest near the surface of the Earth and, gets weaker as we move farther and farther away from the Earth. This force is called the “Field Force” because It acts on all objects whether they are in contact with Earth’s surface or not. So, it is a non-contact force. For example, it acts on an airplane either It is standing on Earths surface or flying in the sky. Gravitational Field Strength:
A body of mass one kilogram (1kg) on Earth experiences a force of about ten Newton (10N) due to Earth’s gravitational, field. This force determines the gravitational field strength which is defined as Gravitational field strength ‘g’ is the gravitational force acting per unit mass. The gravitational field strength ‘g’ is approximately 10 Newton per kilogram 10Nkg. The gravitational field strength ‘g’ is different at different planets. For example, the gravitational field strength ‘g’ on the surface of the Moon is approximately 1.6 Newton per Kilogram 1.6Nkg. Acceleration due to gravity ‘g’ at different planets is shown in the following table.
| Planets | Value of g (m/s²) |
|---|---|
| Earth | 10 |
| Moon | 1.62 |
| Venus | 8.87 |
| Mars | 3.77 |
| Jupitar | 25.95 |
| Mercury | 3.59 |
| Saturn | 11.08 |
| Uranus | 10.67 |
| Neptune | 14.07 |
Does the solar system work in a push pull network?
Gravity keeps things together. It is a force that attracts matter towards it. Anything with mass creates gravity, but the amount of gravity is proportional to the amount of mass. Therefore, Jupiter has a stronger graviational pull than Mercury. Distance also affects the strength of the gravitational force. Therefore, the Earth has a stronger pull on us than Jupiter does, even though Jupitar is as big as over 1300 Eaths. Which we are familiar with gravity impact on us and Earth, this force also has many effects on the entire solar system, too.
CREATES ORBIT:
Gravity keeps things together. It is a force that attracts matter towards it. Anything with mass creates gravity, but the amount of gravity is proportional to the amount of mass. Therefore, Jupiter has a stronger graviational pull than Mercury. Distance also affects the strength of the gravitational force. Therefore, the Earth has a stronger pull on us than Jupiter does, even though Jupitar is as big as over 1300 Eaths. Which we are familiar with gravity impact on us and Earth, this force also has many effects on the entire solar system, too.
One of the most noticeable effects of gravity in the solar system is the orbit of the planets. The sun could hold 13 million Earths to its mass has a strong gravitational pull. When a planet tries to go past the sun at a high rate of speed, gravity grabs the planet and pulls it towards the sun. Likewise, the planets gravity is trying to pull the sun towards it but cant because of the vast difference in mass. The planet keeps moving but is always caught up in the push-pull forces caused by the interaction of these gravitational force, Asa result, the planet begins orbiting the sun. The same phenomenon causes the moon to orbit around the Earth except for the Earths gravitational force, not the suns that keeps it moving around us.
TIDAL HEATING:
Just as the moon orbits the Earth, other planets have moons of their own. The push-pull relationship between the gravitational forces of the planets and their moons causes an effect known as tidal bulges. On Earth, we see these bulges as high and Low tides because they occur over ocean, But on planets or moons without water, tidal bulges can occur over land. In some cases, the bulge created by gravity will be pulled back and forth because the orbit varies in its distance from the primary source of gravity. The pulling causes friction and is known as tidal heating. On lo, one of Jupiter's moons, the tidal heating has caused volcanic activity. This heating may also be responsible for volcanic activity on Saturn's Enceladus and Liquid water underground on Jupiter's Europa.
CREATING STARS:
Giant molecular clouds made up of gas and dust slowly collapse because of the inward pull of their gravity. When these clouds collapse, they form lots of smaller areas of gas and dust that will eventually collapse as well. When these fragments collapse they form stars. Because the fragments from the original GMC stay in the same general area, their collapse causes stars to form clusters.
FORMATION OF PLANETS:
When a star is born, all of the dust and gas not needed in its formation ends up trapped in the orbit of the star. The dust particles have more mass than the gas so they can begin to concentrate in certain areas where they come in contact with other dust grain, These grains are pulled together by their own gravitational forces and kept in orbit by the gravity of the star. As the collection of grains becomes bigger, other forces also begin to act upon it until a planet forms over a very Long period of time.
CAUSE DESTRUCTION:
Because many things in the solar system are held together thanks to the gravitational pull among its component, strong external gravitational forces could pull those components apart thus destroying the object. This happens with moons sometimes. For example, Neptune's Triton is being pulled closer and closer to the planet as it orbits. When the moon gets too dos, perhaps in 100 million to 1 billion years, the planets gravity will pull the moon apart. This effect might also explain the origin of the debris that makes up the rings found around all of the large planets i.e. Jupiter, Saturn, and Uranus.
Q.6) What will be the effect on the gravitational pull between two objects if the medium between them is changed?
Ans) The gravitational force present between the two masses will always remain the same no matter whether the masses are in air, vacuum, water, or separated by some hindrance. Because, the gravitational force is not dependent on the intervening medium. Therefore, there will be no effect on the gravitational putt between two objects if the medium between them is changed.
Q.7) Which force causes the moon to move in orbit around the earth?
Ans) When an object moves in a circle at a constant speed, its direction constantly change, A change in direction causes a change in velocity. This is because velocity is a vector quantity. It has an associated direction as well as am magnitude.
A change in velocity results in acceleration, so an object moving in a circle is accelerating even though its speed may be constant. An object will only accelerate if a resultant force acts on it. For an object moving in a circle, this resultant force is the centripetal force that acts towards the middle of the circle. The gravitational attraction provides the centripetal force needed to keep planets in orbit around the Sun and all types of satellites in orbit around the Earth. The Earth's gravity keeps the Moon orbiting us. It keeps changing the direction of the Moons velocity. This means gravity makes the Moon accelerate all the time, even though its speed remains constant.
Q.8) Define weight. What instrument is used to measure the weight of an object?
Ans) "The measurement of the gravitational force acting on the object".
Mathematically,
w = mg
INSTRUMENT USED TO MEASURE WEIGHT:Spring balance is used to measure the weight of an object. An object of mass 1kg has a weight of 9.8N near the surface of Earth. The objects with larger masses may have larger weights. Our weight varies slightly from place to place, because Earth's gravitational field strength varies at different places. The weight of the object changes as it moves away from the Earth. The weight of the object is different on different planets.
For example, we will have less weight at Moon because Moons gravitational field is weaker than Earth.
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