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प्रश्न
Write the answer of the question with reference to laws of gravitation.
State the universal law of gravitation.
Answer the following question.
State Newton’s 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
How does the force of gravitation between two objects change when the distance between them is reduced to half?
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 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:
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.
The gravitational intensity at the centre of a hemispherical shell of uniform mass density has the direction indicated by the arrow (see Fig 8.12) (i) a, (ii) b, (iii) c, (iv) 0.
A rocket is fired from the earth towards the sun. At what distance from the earth’s centre is the gravitational force on the rocket zero? Mass of the sun = 2 ×1030 kg, mass of the earth = 6 × 1024 kg. Neglect the effect of other planets etc. (orbital radius = 1.5 × 1011 m).
Which of the Kepler’s laws of planetary motion led Newton to establish the inverse-square rule for gravitational force between two bodies ?
Can we apply Newton’s third law to the gravitational force ? Explain your answer.
Universal law of gravitation states that every object exerts a gravitational force of attraction on every other object. If this is true, why don’t we notice such forces ? Why don’t the two objects in a room move towards each other due to this force ?
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?
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.
Which of the following quantities remain constant in a planetary motion (consider elliptical orbits) as seen from the sun?
Three equal masses m are placed at the three corners of an equilateral triangle of side a. Find the force exerted by this system on another particle of mass m placed at (a) the mid-point of a side, (b) at the centre of the triangle.
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.
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.
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.
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 final velocity of the ball on reaching the ground .
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.
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:
Doubled
How will the force of gravitation between two objects change if the distance between them is:
Infinite
Is the law of gravitation applicable in case of the sun and the moon?
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 catch a kicked ball.
Name and state the action and reaction in the following case:
A book lying on a table.
Why does a ball moving on a table top eventually stops?
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?
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.
State Newton's law of gravitation. What is the difference between:
Gravity and gravitation
Show that gravity decreases at higher altitudes.
Mahendra and Virat are sitting at a distance of 1 m from each other.Their masses are 75 kg and 80 kg respectively. What is the gravitational force between them? (G = 6.67 × 10-11 Nm2/kg2)
To project the rockets which of the following principle(s) is /(are) required?
State the universal law of gravitation and derive its mathematical expression.
Give the applications of universal law gravitation.
For the weight of body of mass 5 kg to be zero on equator of the earth, angular velocity of the earth must be (The radius of earth = 6400 km, acceleration due to gravity = 10 m/s2).
The force of gravitation between two bodies of mass 1 kg each separated by a distance of 1 m in vacuum is ____________.
As observed from earth, the sun appears to move in an approximate circular orbit. For the motion of another planet like mercury as observed from earth, this would ______.
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.
Shown are several curves (Figure). Explain with reason, which ones amongst them can be possible trajectories traced by a projectile (neglect air friction).
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.
Give scientific reasons for the following:
Newton's gravitational law is the universal law of gravitation.
Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m under the action of their own mutual gravitational attraction. The speed of each particle will be ______.
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 the mass of one object is doubled and distance remains the same, the gravitational force will:
The acceleration of the Moon towards the Earth is approximately:
