Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
The gravitational potential due to the system is given as \[V = \frac{k}{r^2}\]
Gravitational field due to the system :
\[E = - \frac{dV}{dr}\]
\[ \Rightarrow E = - \frac{d}{dr}\left( \frac{k}{r^2} \right) = - \left( - \frac{2k}{r^3} \right)\]
\[ \Rightarrow E = \frac{2k}{r^3}\]
We can see that for this system , \[E \propto \frac{1}{r^3}\]
This type of system is not possible because \[F_g\] is always proportional to inverse of square of distance(experimental fact).
If there were negative masses, then this type of system is possible.
This system is a dipole of two masses, i.e., two masses, one positive and the other negative, separated by a small distance.
In this case, the gradational field due to the dipole is proportional to \[\frac{1}{r^3}\]
APPEARS IN
संबंधित प्रश्न
If the moon attracts the earth, why does the earth not move towards the moon?
What happens to the force between two objects, if the mass of one object is doubled?
Choose the correct alternative:
Acceleration due to gravity increases/decreases with increasing depth. (assume the earth to be a sphere of uniform density).
Which of the Kepler’s laws of planetary motion led Newton to establish the inverse-square rule for gravitational force between two bodies ?
Write the three laws given by Kepler. How did they help Newton to arrive at the inverse square law of gravity?
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.
Two spherical balls of mass 10 kg each are placed 10 cm apart. Find the gravitational force of attraction between them.
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 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.
Write an expression for the gravitational force of attraction between two bodies of masses m1 and m2 separated by a distance r.
What is the difference between gravity and gravitation?
Answer the following question.
What are the dimensions of the universal gravitational constant?
What do you mean by a gravitational constant?
Choose the wrong option.
Particles of masses 2M, m and M are respectively at points A, B and C with AB = ½ (BC). m is much-much smaller than M and at time t = 0, they are all at rest (Figure). At subsequent times before any collision takes place ______.
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.
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 ______.
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?
