  Patterns of problems

## Gravitation

- It is always better to be prepared. Practice the kind of problems asked in various exams
1
Pattern: Simple problems involving universal law of gravitation.

Description: Any particle of matter in the universe attracts any other with a force varying directly proportional to the product of the masses and inversely proportional to the square of the distance between them.

• Problem to calculate the gravitational force between two bodies.
• Problem to calculate the effect of gravitational force in a system of bodies.
• Problem to find the distance at which gravitational force acting on any mass is zero.
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2
Pattern: Problem based on superposition principle.

Description: Discuss about net force acting on one mass by number of bodies and the concept of negative mass.

• Problem to calculate the force acting on one mass by no. of bodies.
• To find the gravitational force between the solid spherical bodies of uniform density which have cavities in them.
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3
Pattern: Problem based on variation in the value of acceleration due to gravity.

Description: The value of 'g' depends upon the height and the depth on the earth surface. And also upon the latitudinal position on earth.

• To find the value of 'g' at some height above the earth surface.
• To find the value of 'g' at some depth below the earth surface.
• To find the variation of 'g' due to the axial rotation of earth.
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4
Pattern: Problem based on gravitational field and gravitational potential
Description: The gravitational potential at a point in a gravitational field is the work done per unit mass that would have to be done by some externally applied force to bring a massive object to that point from some defined position of zero potential, usually infinity.
1. To find gravitational field due to continuous masses by integration of elemental masses.
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5
Pattern: Problems based on Kepler's law
Description: Kepler's laws of planetary motion state:
• All planets move around the Sun in elliptical orbits, with the Sun as one focus of the ellipse.
• A radius vector joining any planet to the Sun sweeps out equal areas in equal lengths of time.
• The square of the time period of revolution of a planet around the sun in an elliptical orbit is directly proportional to the cube of its semi-major axis