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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
Write the formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth.
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?
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 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?
Can you think of two particles which do not exert gravitational force on each other?
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 be the gravitational potential and gravitational field at a distance r from the centre of a uniform spherical shell. Consider the following two statements :
(A) The plot of V against r is discontinuous.
(B) The plot of E against r is discontinuous.
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
Which of the following quantities remain constant in a planetary motion (consider elliptical orbits) as seen from the sun?
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 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 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 thin spherical shell having uniform density is cut in two parts by a plane and kept separated as shown in the following figure. The point A is the centre of the plane section of the first part and B is the centre of the plane section of the second part. Show that the gravitational field at A due to the first part is equal in magnitude to the gravitational field at B due to the second part.
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.
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.]
The law of gravitation gives the gravitational force between :
Explain the following:
People often shake the branches of a tree for getting down its fruits.
State whether the gravitational force between two masses is attractive or repulsive ?
Write an expression for the gravitational force of attraction between two bodies of masses m1 and m2 separated by a distance r.
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 .
Define one Newton. How much maximum acceleration can it produce in a mass of 1 kg?
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:
Halved
How will the force of gravitation between two objects change if the distance between them is:
Made four times
Is the law of gravitation applicable in case of the sun and the moon?
Why don't you feel the force of attraction between your friend sitting close to you and yourself?
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 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 pull the skin of your arm
What does a force do in the following case?
You apply brakes to a running car.
You can change the direction in which an object is moving by___________.
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?
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.
Is there a gravitational attraction between you and the book? Explain.
State Newton's law of gravitation. What is the difference between:
Gravity and gravitation
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.
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)
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 ____________.
Molecules in air in the atmosphere are attracted by gravitational force of the earth. Explain why all of them do not fall into the earth just like an apple falling from a tree.
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.
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).
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 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:
- 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?
If the mass of one object is doubled and distance remains the same, the gravitational force will:
If the distance between two objects is doubled, the gravitational force becomes:
