Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
- According to Newton’s universal law of gravitation theory, every object in the universe attracts every other object with a definite force. This force is directly proportional to the product of the masses of the two objects and is inversely proportional to the square of the distance between them. The above figure shows two objects with masses m1 and m2 kept at a distance d from each other. Mathematically, the gravitational force of attraction between these two bodies can be written as
`Fα (m_1m_2)/d^2 or F= G (m_1m_2)/d^2`
Here, G is the constant of proportionality and is called the universal gravitational constant. - If the distance between the two bodies is tripled, the gravitational force between them would decrease by a factor of 9 (since force is inversely proportional to the square of the distance). This is because according to the law of gravitation, F ∝ `1/d^2`, so if d becomes 3d, then
`F = G(m_1m_2)/(3d^2) = G(m_1m_2)/(9d^2)` - If the mass of one of the objects is doubled, the gravitational force between them will also double. This is because the force is directly proportional to the masses of the objects. So, F ∝ m1 or F ∝ m2, which means if m1 becomes 2m1,
`F = G(2m_1m_2)/(d^2) = 2G(m_1m_2)/(d^2)`
APPEARS IN
संबंधित प्रश्न
If the moon attracts the earth, why does the earth not move towards the moon?
Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth = 6 × 1024 kg and of the Sun = 2 × 1030 kg. The average distance between the two is 1.5 × 1011 m.
State the universal law of gravitation. Name the scientist who gave this law.
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?
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?
A person brings a mass of 1 kg from infinity to a point A. Initially the mass was at rest but it moves at a speed of 2 m s −1 as it reaches A. The work done by the person on the mass is −3 J. The potential at A is
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.
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.
Explain the following:
People often shake the branches of a tree for getting down its fruits.
Write an expression for the gravitational force of attraction between two bodies of masses m1 and m2 separated by a distance r.
How will the force of gravitation between two objects change if the distance between them is:
Halved
What does a force do in the following case?
You pull the skin of your arm
Is there a gravitational attraction between you and the book? Explain.
The value of universal gravitational constant (G) in the SI unit is ______.
The ______ force is much weaker than other forces in nature.
Give the applications of universal law gravitation.
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).
Ocean tides on Earth are mainly caused by ______.
The acceleration of the Moon towards the Earth is approximately ______.
