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प्रश्न
Write the answer of the question with reference to laws of gravitation.
State the universal law of gravitation.
Answer the following question.
State Newton’s law of gravitation.
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उत्तर
The universal law of gravitation states that every object in the universe attracts every other object with a force called the gravitational force. The force acting between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.
F ∝ m M (masses of two bodies m and M)
F ∝ `1/"d"^2` (d is the distance between the two bodies.)
A and B are two bodies, the distance between which is given as d.
F = force with which one body is attracting the other.
G = proportionality constant.
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संबंधित प्रश्न
Write the formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth.
How does the force of gravitation between two objects change when the distance between them is reduced to half?
What happens to the force between two objects, if the distance between the objects is doubled and tripled?
What happens to the force between two objects, if the masses of both objects are doubled?
Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth = 6 × 1024 kg and of the Sun = 2 × 1030 kg. The average distance between the two is 1.5 × 1011 m.
Answer the following:
You can shield a charge from electrical forces by putting it inside a hollow conductor. Can you shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means?
Answer the following:
An astronaut inside a small space ship orbiting around the earth cannot detect gravity. If the space station orbiting around the earth has a large size, can he hope to detect gravity?
If you compare the gravitational force on the Earth due to the Sun to that due to the Moon, you would find that the Sun’s pull is greater than the Moon’s pull. (You can check this yourself using the data available in the succeeding exercises). However, the tidal effect of the Moon’s pull is greater than the tidal effect of Sun. Why?
Choose the correct alternative:
Acceleration due to gravity increases/decreases with increasing altitude.
Choose the correct answer from among the given ones:
For the problem 8.10, the direction of the gravitational intensity at an arbitrary point P is indicated by the arrow (i) d, (ii) e, (iii) f, (iv) g.
A rocket is fired from the earth towards the sun. At what distance from the earth’s centre is the gravitational force on the rocket zero? Mass of the sun = 2 ×1030 kg, mass of the earth = 6 × 1024 kg. Neglect the effect of other planets etc. (orbital radius = 1.5 × 1011 m).
State Kepler’s law which is represented by the relation r3 ∝ T2.
State and explain Kepler's laws of planetary motion. Draw diagrams to illustrate these laws.
Can two particles be in equilibrium under the action of their mutual gravitational force? Can three particles be? Can one of the three particles be?
Can you think of two particles which do not exert gravitational force on each other?
At noon, the sun and the earth pull the objects on the earth's surface in opposite directions. At midnight, the sun and the earth pull these objects in same direction. Is the weight of an object, as measured by a spring balance on the earth's surface, more at midnight as compared to its weight at noon?
A person brings a mass of 1 kg from infinity to a point A. Initially the mass was at rest but it moves at a speed of 2 m s −1 as it reaches A. The work done by the person on the mass is −3 J. The potential at A is
A person sitting in a chair in a satellite feels weightless because
A body is suspended from a spring balance kept in a satellite. The reading of the balance is W1 when the satellite goes in an orbit of radius R and is W2 when it goes in an orbit of radius 2 −R.
Which of the following quantities remain constant in a planetary motion (consider elliptical orbits) as seen from the sun?
Four particles having masses m, 2m, 3m and 4m are placed at the four corners of a square of edge a. Find the gravitational force acting on a particle of mass m placed at the centre.
Three uniform spheres each having a mass M and radius a are kept in such a way that each touches the other two. Find the magnitude of the gravitational force on any of the spheres due to the other two.
Two concentric spherical shells have masses M1, M2 and radii R1, R2 (R1 < R2). What is the force exerted by this system on a particle of mass m1 if it is placed at a distance (R1+ R2)/2 from the centre?
A solid sphere of mass m and radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in the following figure . A particle of mass m' is placed on the line joining the two centres at a distance x from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if (a) r < x < 2r, (b) 2r < x < 2R and (c) x > 2R.
A thin spherical shell having uniform density is cut in two parts by a plane and kept separated as shown in the following figure. The point A is the centre of the plane section of the first part and B is the centre of the plane section of the second part. Show that the gravitational field at A due to the first part is equal in magnitude to the gravitational field at B due to the second part.
The gravitational field in a region is given by \[E = \left( 2 \overrightarrow{i} + 3 \overrightarrow{j} \right) N {kg}^{- 1}\] . Show that no work is done by the gravitational field when a particle is moved on the line 3y + 2x = 5.
[Hint : If a line y = mx + c makes angle θ with the X-axis, m = tan θ.]
Explain the following:
People often shake the branches of a tree for getting down its fruits.
A ball is thrown vertically upwards. It goes to a height 20 m and then returns to the ground. Taking acceleration due to gravity g to be 10 ms-2, find: the initial velocity of the ball.
A ball is thrown vertically upwards. It goes to a height 20 m and then returns to the ground. Taking acceleration due to gravity g to be 10 ms-2 , find :
the total time of journey of the ball .
Multiple Choice Question. Select the correct option.
The mass of earth is 6 × 1024 kg and radius of earth is 6.4 × 106 m. The magnitude of force between the mass of 1 kg and the earth is:
The acceleration produced by a force in an object is directly proportional to the applied _________ And inversely proportional to the _________ Of the object.
How will the force of gravitation between two objects change if the distance between them is:
Halved
All objects in the universe attract each other along the line joining their________.
The force of attraction between any two material objects is called __________.
Is the law of gravitation applicable in case of the sun and the moon?
A ball is thrown up with a speed of 4.9 ms-1.
Calculate the maximum height it would gain before it begins to fall.
A ball is thrown up with a speed of 4.9 ms-1.
Calculate the time it takes to reach this height.
Where will you weigh more: at the moon's surface or at the earth's surface?
What does a force do in the following case?
You twist a piece of rubber.
What does a force do in the following case?
You catch a kicked ball.
Name and state the action and reaction in the following case:
A book lying on a table.
Name and state the action and reaction in the following case:
A person walking on the ground.
Name and state the action and reaction in the following case:
Hammering a nail.
Two equal and opposite forces acting at the same point on a stationary body. Will the body move? Give reason to explain your answer.
State the law of gravitation. Why is it called universal?
What is the difference between gravity and gravitation?
State Newton's law of gravitation. What is the difference between:
Gravity and gravitation
State Newton's law of gravitation. What is the difference between:
g and G?
Solve the following problem.
Find the gravitational force between the Sun and the Earth.
Given Mass of the Sun = 1.99 × 1030 kg
Mass of the Earth = 5.98 × 1024 kg
The average distance between the Earth and the Sun = 1.5 × 1011 m.
The _______ force is much weaker than other forces in nature.
As observed from earth, the sun appears to move in an approximate circular orbit. For the motion of another planet like mercury as observed from earth, this would ______.
Molecules in air in the atmosphere are attracted by gravitational force of the earth. Explain why all of them do not fall into the earth just like an apple falling from a tree.
We can shield a charge from electric fields by putting it inside a hollow conductor. Can we shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means?
The gravitational force between a hollow spherical shell (of radius R and uniform density) and a point mass is F. Show the nature of F vs r graph where r is the distance of the point from the centre of the hollow spherical shell of uniform density.
Complete the chart below.
| F(N) | M1(kg) | M2(kg) | D(m) |
| (a) | 50 | 84 | 02 |
| 16 × 109 | 1.63 × 1022 | (b) | 34 |
Two particles of equal mass 'm' go around a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle with respect to its centre of mass is ______.
Who measured the value of the Universal Gravitational Constant G using the Cavendish balance?
A hollow spherical shell of uniform density exerts what gravitational force on a point mass placed inside it?
Newton formulated the Universal Law of Gravitation by combining the ideas of which two scientists with his own Laws of Motion?
The gravitational force between two objects acts in which direction?
