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
Answer the following:
An astronaut inside a small space ship orbiting around the earth cannot detect gravity. If the space station orbiting around the earth has a large size, can he hope to detect gravity?
Choose the correct alternative:
Acceleration due to gravity increases/decreases with increasing altitude.
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 ?
Explain the following:
People often shake the branches of a tree for getting down its fruits.
State whether the gravitational force between two masses is attractive or repulsive ?
The acceleration produced by a force in an object is directly proportional to the applied _________ And inversely proportional to the _________ Of the object.
Distinguish between gravity and gravitation
Is the law of gravitation applicable in case of the sun and the moon?
Why don't you feel the force of attraction between your friend sitting close to you and yourself?
What does a force do in the following case?
You apply brakes to a running car.
What does a force do in the following case?
You catch a kicked ball.
State the law of gravitation. Why is it called universal?
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 ________.
State Newton's law of gravitation. What is the difference between:
Gravity and gravitation
What do you mean by a gravitational constant?
Solve the following problem.
Calculate the acceleration due to gravity at a height of 300 km from the surface of the Earth. (M = 5.98 × 1024 kg, R = 6400 km).
Law of gravitation gives the gravitational force between
If three equal masses m are placed at the three vertices of an equilateral triangle of side 1/m then what force acts on a particle of mass 2m placed at the centroid?
If the mass of one object is doubled and distance remains the same, the gravitational force will:
If the distance between two objects is doubled, the gravitational force becomes:
