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Answer the following question. State Newton’s law of gravitation and express it in vector form.

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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

  1. 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.
  2. 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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पाठ 5: Gravitation - Exercises [पृष्ठ ९७]

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बालभारती Physics [English] Standard 11 Maharashtra State Board
पाठ 5 Gravitation
Exercises | Q 2. (xii) | पृष्ठ ९७

संबंधित प्रश्‍न

What is the importance of the universal law of gravitation?


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?


Choose the correct alternative:

 Acceleration due to gravity increases/decreases with increasing altitude.


State two applications of universal law of gravitation.


Write the three laws given by Kepler. How did they help Newton to arrive at the inverse square law of gravity?


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?


Two spherical balls of mass 10 kg each are placed 10 cm apart. Find the gravitational force of attraction between them.


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.


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 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.


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 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.


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:


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


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.


What does a force do in the following case?
You twist a piece of rubber.


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 ________.


Is there a gravitational attraction between you and the book? Explain.


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

 


State Newton’s universal law of gravitation. Express it with the mathematical form of force of 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.


Give scientific reasons for the following:

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


Complete the chart below.

F(N) M1(kg) M2(kg) D(m)
(a) 50 84 02
16 × 109 1.63 × 1022 (b) 34

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:

  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?

Who measured the value of the Universal Gravitational Constant G using the Cavendish balance?


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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