Download gravitation-1 - Physics Point in Gurgaon

PHYSICS POINT
ASSIGNMENT Gravitation
-----------------------------------------------------------------------------------------------------------------------------------------Very Short Answer Type Question
(1 MARK)
1. Give two characteristics of gravitational force.
2. An artificial satellite is at a height of 36,500 km above earth’s surface. What is the work
done by earth’s gravitational force in keeping it in its orbit?
3. Define gravitational potential at a point.
4. What is the reason for absence of atmosphere in some planets?
5. What are the factors affecting the value of G?
6. What is the orbital velocity for a satellite orbiting close to the surface of earth?
7. What is the basis for the second Law of Kepler?
8. What does spring balance measure: Mass or Weight?
9. What is a geostationary satellite? Is it same as geo-synchronous satellite?
10. Can a satellite be in an orbit in a plane not passing through the earth’s centre? Explain your
answer.
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(2 MARK)
What is the gravitational force on a body inside a spherical shell? Why is it so?
What is escape velocity. Derive an expression for the same.
Is it possible to place a satellite, so that it is always over New Delhi? Why?
The radius of the earth is reduced by 4%. The mass of the earth remains unchanged. What
will be the change in escape velocity?
Satellite A is in a certain circular orbit about a planet, while satellite B is in a larger circular
orbit. Which satellite has (i) the longer period and (ii) the greater speed?
If the radius of the earth were increased by a factor of 3, by what factor would its density
have to be changed to keep ‘g’ the same?
State Kepler’s laws of planetary motion and deduce Newton’s Law of gravitation rom them.
Discuss the variation of ‘g’ with depth. What happens to ‘g’ at the centre of the earth?
Find the potential energy of a system of four particles placed at the vertices of a square of
side l. Also, obtain the potential at the centre of the square.
The mass and diameter of a planet are twice of those of the earth. What will be the period
of oscillation of a pendulum on this planet, if it is a second’s pendulum on the earth?
Short Answer Type Questions
(3 MARK)
1. Define gravitational potential energy of a body. Derive an expression for the gravitational
potential energy of a body of mass ‘m’ located at a distance ‘r’ from the centre of the earth.
2. Prove that gravitational potential difference is the work done in carrying a unit mass from
one point to another.
3. The kinetic energy associated with a satellite is E. What is the total energy associated?
4. To what height a mass can go, when sent up with a velocity half of the escape velocity?
5. Briefly describe the Cavendish torsion balance. How is it used to measure g?
6. Three masses, each equal to M, are placed at the three corners of a square of side ‘a’.
Calculate the force of attraction on unit mass at the fourth corner.
7. Define gravitational potential and gravitational field intensity. Give their units. Also write the
relation between them.
8. State Newton’s law of Gravitation. Find the percentage decrease in the weight of the body
when taken to a height of 16 km. above the surface of the earth. Radius of the earth is 6400
km.
9. Considering a nearly circular orbit, prove that the square of time period of a planet is
proportional to the cube of its radius.
10. What is the effect of rotation on the value of ‘g’? Derive the relation.
Long Answer Type Questions
(5 MARK)
1. State Kepler’s laws on planetary motion. Explain the way the three laws can be proved.
2. What is escape velocity? Obtain the expression for the escape velocity on earth. Why is it
that there is no atmosphere on the moon? Explain.
3. What is the difference between gravitational potential and gravitational potential energy.
Derive an expression for gravitational potential energy of a body.
4. Derive a relation for work done in a gravitational field. Using it, (i) find potential difference
between a pair of points. (ii) express whether gravitational force is conservation or nonconservative.
5. Two heavy spheres each of mass 100 kg and radius 0.10 m are placed 1.0 m apart on a
horizontal table. What is the gravitational force and potential at the mid point of the line
joining the centres of the spheres? Is an object placed at that point in equilibrium? If so, is
the equilibrium stable or unstable?
6. A body weighs 63 N on the surface on the earth. What is the gravitational force on it due to
the earth at a height equal to half the radius of the earth?
7. Assuming the earth to be a sphere of uniform mass density, how much would a body weigh
half way down to the centre of the earth if it weighed 250 N on the surface?
8. How will you ’weigh the Sun’, that is, estimate its mass? The mean orbital radius of the earth
around the sun is 1.5 x 108 km.
9. The moon takes about 27 days to complete one orbit around the earth. The orbit is nearly a
circle of radius 3.8 x 108 m. Calculate the mass of the earth from this data.
10. The escape speed of a projectile on the earth’s surface is 11.2 kms-1. A body is projected out
with thrice this speed. What is the speed of the body for away from the earth? Ignore the
presence of the sun and other planets.
BY: Rajesh sir 981010 9161