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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Write the answer of the question with reference to laws of gravitation. State the universal law of gravitation.

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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.

नियम
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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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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Gravitation - Exercises [पृष्ठ ९७]

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संबंधित प्रश्‍न

How does the force of gravitation between two objects change when the distance between them is reduced to half?


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).


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 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:

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?


Can we apply Newton’s third law to the gravitational force ? Explain your answer.


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?


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?


Let V and E represent the gravitational potential and field at a distance r from the centre of a uniform solid sphere. Consider the two statements:
(A) the plot of V against r is discontinuous.
(B) The plot of E against r is discontinuous.


Inside a uniform spherical shell
(a) the gravitational potential is zero
(b) the gravitational field is zero
(c) the gravitational potential is same everywhere
(d) the gravitational field is same everywhere


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 small bodies of masses 10 kg and 20 kg are kept a distance 1.0 m apart and released. Assuming that only mutual gravitational forces are acting, find the speeds of the particles when the separation decreases to 0.5 m.


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 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 tunnel  is dug along a chord of the earth at a perpendicular distance R/2 from the earth's centre. The wall of the tunnel may be assumed to be frictionless. Find the force exerted by the wall on a particle of mass m when it is at a distance x from the centre of the tunnel.


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.]


State whether the gravitational force between two masses is attractive or repulsive ?  


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 final velocity of the ball on reaching the ground .


Who stated the law of gravitation?


Distinguish between gravity and gravitation


How will the force of gravitation between two objects change if the distance between them is:
Almost zero


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.


At what height above the earth's surface would the value of acceleration due to gravity be half of what it is on the surface? Take the radius of earth to be R.


A force can produce ________, In an object at rest. It can __________ an object and change its __________ of motion.


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:
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.


What is the difference between gravity and gravitation?


Explain why:
The atmosphere does not escape.


Does the force of the earth's gravitation affect the motion of the moon? Explain your answer with reasons.


State Newton's law of gravitation. What is the difference between:
g and G?


The distance-time values for an object moving along straight line are given below:

Time (s) Distance (m)
0 0
1 1
2 8
3 27

 


What do you mean by a gravitational constant?


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.


State the universal law of gravitation and derive its mathematical expression.


Law of gravitation gives the gravitational force between


Three uniform spheres, each having mass m and radius r, are kept in such a way that each touches the other two. The magnitude of the gravitational force on any sphere due to the other two is


Choose the wrong option.


Particles of masses 2M, m and M are respectively at points A, B and C with AB = ½ (BC). m is much-much smaller than M and at time t = 0, they are all at rest (Figure). At subsequent times before any collision takes place ______.


If the law of gravitation, instead of being inverse-square law, becomes an inverse-cube law- ______.

  1. planets will not have elliptic orbits.
  2. circular orbits of planets is not possible.
  3. projectile motion of a stone thrown by hand on the surface of the earth will be approximately parabolic.
  4. there will be no gravitational force inside a spherical shell of uniform density.

How is the gravitational force between two point masses affected when they are dipped in water keeping the separation between them the same?


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.


Give scientific reasons for the following:

Newton's gravitational law is the universal law of gravitation.


Answer the following questions in reference to the figure below:

  1. Which relation is shown in the figure?
  2. What will happen if the mass of one of the objects is doubled?

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 ______.


Observe the figure and answer the questions:

  1. State Newton's universal law of gravitation.
  2. If the distance between the two bodies is tripled, how will the gravitational force between them change?
  3. What will happen to gravitational force, if mass of one of the object is doubled?

The Superposition Principle states that the net gravitational force on an object is ______.


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?


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