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?
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
How does the force of gravitation between two objects change when the distance between them is reduced to half?
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?
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 is independent of mass of the earth/mass of the body.
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 ?
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?
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
Consider a planet moving in an elliptical orbit round the sun. The work done on the planet by the gravitational force of the sun
(a) is zero in any small part of the orbit
(b) is zero in some parts of the orbit
(c) is zero in one complete revolution
(d) is zero in no part of the motion.
Derive an expression for the gravitational field due to a uniform rod of length L and mass M at a point on its perpendicular bisector at a distance d from the centre.
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.]
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 total time of journey of the ball .
Define one Newton. How much maximum acceleration can it produce in a mass of 1 kg?
How will the force of gravitation between two objects change if the distance between them is:
Halved
Show that gravity decreases at higher altitudes.
The _______ force is much weaker than other forces in nature.
Three uniform spheres, each having mass m and radius r, are kept in such a way that each touches the other two. The magnitude of the gravitational force on any sphere due to the other two 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 ______.
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.
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.
