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प्रश्न
Write the answer of the question with reference to laws of gravitation.
State the universal law of gravitation.
State Newton’s law of gravitation.
State Newton’s Universal 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
What is the magnitude of the gravitational force between the earth and a 1 kg object on its surface? (Mass of the earth is 6 × 1024 kg and radius of the earth is 6.4 × 106 m).
The earth and the moon are attracted to each other by gravitational force. Does the earth attract the moon with a force that is greater or smaller or the same as the force with which the moon attracts the earth? Why?
If the moon attracts the earth, why does the earth not move towards the moon?
What happens to the force between two objects, if the mass of one object is doubled?
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?
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?
State two applications of universal law of gravitation.
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?
The weight of an object is more at the poles than at the equator. Is it beneficial to purchase goods at equator and sell them at the pole? Does it matter whether a spring balance is used or an equal-beam balance is used?
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
Consider a planet moving in an elliptical orbit round the sun. The work done on the planet by the gravitational force of the sun
(a) is zero in any small part of the orbit
(b) is zero in some parts of the orbit
(c) is zero in one complete revolution
(d) is zero in no part of the motion.
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.
Four particles of equal masses M move along a circle of radius R under the action of their mutual gravitational attraction. Find the speed of each particle.
Derive an expression for the gravitational field due to a uniform rod of length L and mass M at a point on its perpendicular bisector at a distance d from the centre.
A tunnel is dug along a diameter of the earth. Find the force on a particle of mass m placed in the tunnel at a distance x from the centre.
A uniform metal sphere of radius a and mass M is surrounded by a thin uniform spherical shell of equal mass and radius 4a (In the following figure). The centre of the shell falls on the surface of the inner sphere. Find the gravitational field at the points P1 and P2 shown in the figure.
A particle of mass 100 g is kept on the surface of a uniform sphere of mass 10 kg and radius 10 cm. Find the work to be done against the gravitational force between them to take the particle away from the sphere.
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.]
The mass of moon is about 0.012 times that of earth and its diameter is about 0.25 times that of earth. The value of G on the moon will be:
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 .
The acceleration produced by a force in an object is directly proportional to the applied _________ And inversely proportional to the _________ Of the object.
The force of attraction between any two material objects is called __________.
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.
Prove that the time of ascent is equal to the time of descent.
Where will you weigh more: at the centre of the earth or at the surface of the earth?
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 pull the skin of your arm
What does a force do in the following case?
You apply brakes to a running car.
What does a force do in the following case?
You catch a kicked ball.
You can change the direction in which an object is moving by___________.
Name and state the action and reaction in the following case:
A person walking on the ground.
What is the difference between gravity and gravitation?
Gravity is another kind of ________. It exerts all through the ________. The Sun's gravity keeps the ___________ in their orbits. Gravity can only be felt with very large ________.
Explain why:
The atmosphere does not escape.
Explain the difference between g and G.
An apple falls towards the earth due to its gravitational force. The apple also attracts the earth with the same force. Why do we not see the earth rising towards the apple? Explain.
Show that gravity decreases at higher altitudes.
Answer the following question.
What are the dimensions of the universal gravitational constant?
Answer the following question.
State Newton’s law of gravitation and express it in vector form.
The ______ force is much weaker than other forces in nature.
To project the rockets which of the following principle(s) is /(are) required?
State the universal law of gravitation and derive its mathematical expression.
Different points in earth are at slightly different distances from the sun and hence experience different forces due to gravitation. For a rigid body, we know that if various forces act at various points in it, the resultant motion is as if a net force acts on the c.m. (centre of mass) causing translation and a net torque at the c.m. causing rotation around an axis through the c.m. For the earth-sun system (approximating the earth as a uniform density sphere).
Choose the wrong option.
If the law of gravitation, instead of being inverse-square law, becomes an inverse-cube law- ______.
- planets will not have elliptic orbits.
- circular orbits of planets is not possible.
- projectile motion of a stone thrown by hand on the surface of the earth will be approximately parabolic.
- there will be no gravitational force inside a spherical shell of uniform density.
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.
Answer the following questions in reference to the figure below:
- Which relation is shown in the figure?
- What will happen if the mass of one of the objects is doubled?
Find the gravitational force of attraction between the ring and sphere as shown in the diagram, where the plane of the ring is perpendicular to the line joining the centres. If `sqrt8` R is the distance between the centres of a ring (of mass 'm')and a sphere (mass 'M') where both have equal radius 'R'.
If three equal masses m are placed at the three vertices of an equilateral triangle of side 1/m then what force acts on a particle of mass 2m placed at the centroid?
Observe the figure and answer the questions:
- State Newton's universal law of gravitation.
- If the distance between the two bodies is tripled, how will the gravitational force between them change?
- What will happen to gravitational force, if mass of one of the object is doubled?
A hollow spherical shell of uniform density exerts what gravitational force on a point mass placed inside it?
For an object outside a uniform solid sphere, from where is the sphere's mass considered to act?
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?
