Hots Questions

## Gravitation

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1
Calculate gravitational force between two objects.
A uniform ring of mass and radius is placed directly above a uniform sphere of mass and of radius . The center of the ring is at a distance of from the center of the sphere. The gravitational attraction between the sphere and ring is
2
Discuss about net force acting on one mass by number of bodies
Two stationary particles of masses and are at distance d apart. A third particle, lying on the line joining the particles, experiences no resultant gravitational force. The distance of this particle from is
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3
We have given a system of two bodies having gravitational pull in between them. A third mass is introduced in in the system which nullifies the gravitation effect. Let's see how the masses are positioned.
Two point masses and are placed at a distance apart. Another point mass is placed in between on the line joining them so that the net gravitational force acting on it due to masses and is zero. The magnitude of gravitational force acting due to mass on mass will be
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4
Concept of negative mass to find gravitational field.
Inside a uniform sphere of density there is a spherical cavity whose centre is at a distance  from the centre of the sphere. Find the strength  of the gravitational field inside the cavity.
5
Problem on acceleration due to gravity and how it varies from one heavenly body to another.
The ratio of radii of the earth to another planet is and the ratio of their mean densities is . If an astronaut can jump to a maximum height of on the earth, with the same effort, the maximum height he can jump on the planet is
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6
Variation in the value of 'g' with height and depth.
A planet has a core and on outer shell of radii and respectively. The density of the core is and that of outer shell is . The acceleration due to gravity at the surface of planet is same as that at depth . The ratio of and is . Find .
7
Understand and calculate variation in time period of a pendulum due to change in acceleration due to gravity.
A pendulum that beats seconds on the surface of the earth were taken to a depth of th the radius of the earth. Its time period of oscillation will be
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A simple pendulum has a time period of on the surface of the earth. On another planet whose density is same that of earth but radius is 4 times then time period of this simple pendulum is then x is :
8
Find gravitational field due to a continuous mass system with variable mass density.
A straight rod of length extends from to . The linear mass density of the rod varies with x-coordinate is . The gravitational force experienced by a point mass at is
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9
Find gravitational field due to a sphere at a point outside the sphere and at a point inside the sphere.
A uniform sphere has a mass  and radius . Find the pressure  inside the sphere, caused by gravitational compression, as a function of the distance  from its centre. Evaluate  at the centre of the Earth, assuming it to be a uniform sphere.
10
Solve numerical on Kepler's laws.
The Jupiter's period of revolution around the Sun is times that of the Earth. Assuming the planetary orbits to be circular, find how many times the distance between the Jupiter and the Sun exceeds that between the Earth and the Sun.
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times
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times
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times
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times
11
Find orbital speed of satellites in circular orbits.
An artificial satellite is launched into a circular orbit around the Earth with velocity v relative to the reference frame moving translationally and fixed to the Earth's rotation axis. The distance from the satellite to the Earth's surface. Find .  The radius of the Earth  and the free-fall acceleration on its surface are supposed to be known.