Question

Define newton's law of gravitation

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Answer 1

Gravity:

➟ The gravitational force of earth is known as gravity i.e., gravity is the force by which earth pulls a body toward it's centre.

➟ The acceleration produced in a body due to force of gravity is known as acceleration due to gravity. Acceleration due to gravity is denoted by “g”. And g's value is 9.8 m/s².

➣ Acceleration due to gravity is independent of shape, mass and size of the mass of the body.

➟ Gravitation- Every body attract other body by a force called force of gravitation.

➣ Newton's law of gravitation- The force of gravitational attraction between two points bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Considering two points ${\sf{m_{1} \: and \: m_{2}}}$ are placed at a distance ${\sf{r}}$ The force of gravitational attraction between them, ${\sf{F \: = G\dfrac{m_{1} m_{2}}{r^{2}}}}$

Here ${\sf{G}}$ is constant called universal gravitational constant. The value of G is ${\sf{6.67 \times 10^{-11} Nm^{2}/kg^{2}}}$

Additional information:

♛ Work - If a body get displaced when a force acts on it, work it said to be done. Work is measured by the product of force and displacement of the body along the direction of force. If a body get displaced by S when a force F act's on it, then the work W = ${\red{\bf{FS \: cos \theta}}}$

[Where, ∅ denotes angle between force and displacement]

If both force and displacement are in the same direction, then W = FS.

Work is a scaler quantity and it's SI unit is joules.

♛ Energy = Capacity of doing work by a body is called it's energy. Energy is a scaler quantity & it's SI unit is ${\red{\bf{joule}}}$ Energy developed in a body due to work done on it is called mechanical energy. Mechanical energy is of two types –

• Potential energy
• Kinetic energy

➜ Potential energy = The capacity of doing work developed in a body due to it's position or configuration is known as potential energy like, ⑴ energy of stretched or compressed string ⑵ energy of spring in a watch ⑶ energy of water collected at a height.

PE of a body is the gravitational field of earth is ${\red{\bf{mgh}}}$

[Where, m denotes mass , g denotes acceleration due to gravity and h denotes height of the body from the surface of the earth].

➜ Kinetic energy = Energy posses by a body due to it's motion is called kinetic energy of the body. If a body of mass is moving with speed then kinetic energy of body is ${\red{\bf{\dfrac{1}{2}mv^{2}}}}$

[Where, m denotes mass and v denotes speed].

Rєlαtíσn вєtwєєn mσmєntum αnd kínєtíc єnєrgч –

${\red{\bf{K.E \: = \: \dfrac{p^{2}}{2m}}}}$

[Where, p = momentum = mv]

Answer 2

Gravity :

• Gravity is a force of attraction that exists between any two masses, any two bodies, any two particles. Gravity is not just the attraction between objects and the Earth.

• It is an attraction that exists between all objects, everywhere in the universe... where G is called the Gravitational Constant.

Force of gravity :

• On Earth all bodies have a weight, or downward force of gravity, proportional to their mass, which Earth's mass exerts on them.

• Gravity is measured by the acceleration that it gives to freely falling objects. At Earth's surface the acceleration of gravity is about 9.8 metres (32 feet) per second per second.

⟹ The mathematical formula for gravitational force is F=GMmr2 F = G Mm r 2 where G is the gravitational constant.

➟ Gravity is measured by the acceleration that it gives to freely falling objects.

➟ At Earth's surface the acceleration of gravity is about 9.8 metres (32 feet) per second per second.

$\color{lime} ★ \color{whte}newton's \: law \: of \: gravitation -$

➜ Newton’s Law of Universal Gravitation states that every particle attracts every other particle in the universe with a force that is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.

➜ The universal gravitation equation thus takes the form :-

$\color{yellow}F∝ \: \frac{m1m2} {r2} \implies \: F = \: G \: \frac {m1m2} {r2}$

➜ Sir Isaac Newton put forward the universal law of gravitation in 1687 and used it to explain the observed motions of the planets and moons.

More Information:

Newton’s conclusion about the magnitude of gravitational forces is summarized symbolically as -

$\big \color{red}F = G\times \frac{m1m2}{r2}$

where,

• F is the gravitational force between bodies.

• m¹ is the mass of one of the objects.

• m² is the mass of the second object.

• r is the distance between the centres of two objects.

• G is the universal gravitational constant.

➜ The constant proportionality (G) in the above equation is known as the universal gravitation constant. The precise value of G was experimentally determined by Henry Cavendish in the century after Newton’s death.

The value of G is found to be G = 6.673 x 10-11 N m²/kg².

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