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

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प्रश्न

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

लघु उत्तरीय
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उत्तर

  1. Statement: Gravitational force between two bodies in the universe is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
  2. The mathematical equation for the law is given as, F = G`("m"_1"m"_2)/"r"^2` where G is universal gravitational constant, m1 and m2 are masses and r is the distance between two masses.
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अध्याय 1: Gravitation - Answer the Following

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).


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?


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 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.


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


A semicircular wire has a length L and mass M. A particle of mass m is placed at the centre of the circle. Find the gravitational attraction on the particle due to the wire.


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 ?  


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


Why don't you feel the force of attraction between your friend sitting close to you and yourself?


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


Name and state the action and reaction in the following case:
Hammering a nail.


The _______ force is much weaker than other forces in nature.


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).


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

Write the answer of the question with reference to laws of gravitation.

Write the value of the universal gravitational constant.


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