Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let us consider the diagram of a spherical shell having uniform density (ρ).
Mass of the shell = (Density) × (Volume)
`M = (ρ) xx 4/3 πR^3`
Therefore, the gravitational force between the hollow shell and point mass is`F = (GMm)/r^2` where M is the mass of the hollow spherical shell and m is the mass of point mass.
Therefore, the mass is distributed on the surface of the sphere only, then F = 0 for 0 < r < R (i.e., force inside the shell is zero)
And `F = (GM)/r^2 for `r ≥ R`
The variation of F versus r is shown in the diagram. Force is maximum at the surface of shell and it is zero if r tends to infinity.
APPEARS IN
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 is the magnitude of the gravitational force between the earth and a 1 kg object on its surface? (Mass of the earth is 6 × 1024 kg and radius of the earth is 6.4 × 106 m).
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?
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.
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
The law of gravitation gives the gravitational force between :
State whether the gravitational force between two masses is attractive or repulsive ?
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:
Almost zero
Why don't you feel the force of attraction between your friend sitting close to you and yourself?
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 the difference between g and G.
Is there a gravitational attraction between you and the book? Explain.
What do you mean by a gravitational constant?
State Newton's universal law of gravitation. Express it with the mathematical form of force of gravitation?
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 acceleration of the Moon towards the Earth is approximately:
If the distance between two objects is doubled, the gravitational force becomes:
