Difficult Questions

Gravitation

- Are you well prepared? Practice hard questions to be more confident about the chapter
1
Problems involving universal law of gravitation.
Two lead balls of masses and having radii and are separated by . If they attract each other by gravitational force, the distance covered by small sphere before they touch each other is:
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2
Two bodies separated at some distance have gravitational force of attraction. Find the separation in between them so that gravitation force is maximum.
Mass is divided into two parts and . For a given separation, the value of for which the gravitational force of attraction between the two pieces becomes maximum is :
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3
Discuss about net force acting on one mass by number of bodies.
Four similar particles of mass m are orbiting in a circle of radius r in the same angular direction because of their mutual gravitational attractive force. Velocity of a particle is given by.
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4
Problem on superposition principle.

Four particles having masses m,2m,3m and 4m are placed at the four corners of a square of edge a.

Find gravitational force acting on a particle of mass m place at the center.

5
Effect of gravitational force on each of bodies so that they are revolve in a circular orbit circumscribing the triangle.
Three identical particles each of mass are arranged at the corners of an equilateral triangle of side . If they are to be in equilibrium, the speed with which they must revolve under the influence of one another's gravity in a circular orbit circumscribing the triangle is
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6
Concept of negative mass to find gravitational field.
A solid sphere of uniform density and radius R applies a gravitational force of attraction equal to  on a particle placed at A, distant from the center of the sphere. A spherical cavity of radius is now made on the sphere with cavity now applies a gravitational force. Then  will be
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7
Variation In Value Of Acceleration Due To Gravity.
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 .
8
Finding the vector sum of gravitational force on a mass due to a system of masses.
Three particles, each of mass are situated at the vertices of an equilateral triangle of side . The only forces acting on the particles are their mutual gravitational forces. It is desired that each particle should move in a circle while maintaining the original mutual separation . Then their time period of revolution is :
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9
Find work done in assembling a continuous mass system or find energy of gravitational interaction.
If the proper potential energy of gravitational interaction of matter forming a thin uniform spherical layer of mass and radius is given as . Find
10
Solve numerical on Kepler's laws.
If a planet were suddenly stopped in its orbit supposed to be circular, show that it would fall into the sun in a time , where is the time period of revolution.
11
Find orbital speed of satellites in circular orbits.
Find the orbital speed of each moon such that they maintain this configuration as . Find