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प्रश्न
Answer the following question.
State Newton’s law of gravitation and express it in vector form.
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उत्तर
- Statement:
Every particle of matter attracts every other particle of matter with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. - In vector form, it can be expressed as,
`vec"F"_21 = "G" ("m"_1"m"_2)/"r"^2(- hat"r"_21)`
where, `hat"r"_21` is the unit vector from m1 to m2. The force `vec"F"_21` is directed from m2 to m1.
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संबंधित प्रश्न
Write the answer of the question with reference to laws of gravitation.
State the universal law of gravitation.
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).
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?
What happens to the force between two objects, if the distance between the objects is doubled and tripled?
What is the importance of the universal law of gravitation?
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.
State Kepler’s law which is represented by the relation r3 ∝ T2.
Which of the Kepler’s laws of planetary motion led Newton to establish the inverse-square rule for gravitational force between two bodies ?
Suppose the gravitational potential due to a small system is k/r2 at a distance r from it. What will be the gravitational field? Can you think of any such system? What happens if there were negative masses?
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.
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 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.
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:
Made four times
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.
Where will you weigh more: at the moon's surface or at the earth's surface?
What is meant by the equation :
`g= Gxxm/r^2`
where the symbols have their usual meanings.
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.
State the law of gravitation. Why is it called universal?
Is there a gravitational attraction between you and the book? Explain.
Give the applications of universal law gravitation.
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.
Six point masses of mass m each are at the vertices of a regular hexagon of side l. Calculate the force on any of the masses.
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?
Newton formulated the Universal Law of Gravitation by combining the ideas of which two scientists with his own Laws of Motion?
