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
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.
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.
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.
The law of gravitation gives the gravitational force between :
Who stated the law of gravitation?
Distinguish between gravity and gravitation
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?
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:
Hammering a nail.
Is there a gravitational attraction between you and the book? Explain.
Does the force of the earth's gravitation affect the motion of the moon? Explain your answer with reasons.
Answer the following question.
What are the dimensions of the universal gravitational constant?
The value of universal gravitational constant (G) in the SI unit is ______.
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.
Two particles of equal mass 'm' go around a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle with respect to its centre of mass is ______.
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'.
The gravitational force between two objects acts in which direction?
