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Syllabus

state and prove work-energy theorem.

Establish a relationship between g and G.

relation between escape velocity and orbital velocity

what is gravitational field strength of a planet ? where the weight 60 kg attronomes is 300 N ?

if earth were suddenly shrink to half of its present radius without change in mass,what is the effect on duration of days?

where is the value of g maximum and minimum at the surface of 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

a rocket is launched vertically from the surface of the earth with initial speed of 10 km/s . how far above the earth's surface will the rocket go?

How much above the surface of earth does the acceleration due to gravity reduces by 36% of its value on the suraface of earth. Radius of earth = 6400 km.

How far from Earth must a body be along a line towards the Sun so that sun's gravitational pull on it balances that of Earth. Distance between Sun and Earth's center is 1.5*10

^{10}km. Mass of Sun is 3.24*10^{5}times mass of Earth.what is stokes law ? What is terminal velocity?

The gravitational field in a region is given by E=(2i^+3j^)N/Kg.Show that no work is done by the gravitational field when a particle is moved on the line 3y+2x=5.Q. A disc of mass m and radius 'R' is attached to a rectangular plate of the same mass breadth R and length 2R as shown in the figure. Find the moment of inertia of this system about the axis XX' passing through the centre of the disc and along the plane.

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.

A particle is projected vertically up with velocity v=(4gRe/3)

^{1/2 }from earth surface. The velocity of particle at height equal to half of the maximum height reached by it .....?^{3}kg from a circular orbit of radius 2R to that of radius 3R. Given mass of earth, M=6x10^{24}kg and radius of earth, R=6.4x10^{6}m1. State Newton's law of gravitation. Hence define universal gravitational constant. Give thevalue and dimensions of G.

2. Define acceleration due to gravity. Show that the value of 'g' decreases with altitude or height.

3. Discuss the variation of ‘g' with depth. What happens to 'g' at the centre of earth?

4. Write down the formula of gravitational potential energy and obtain from it an expression for

gravitational potential.

5. What do you mean by gravitational potential energy of a body? Obtain an expression for it for

a body of mass m lying at distance r from the centre of the earth.

6. Define the term orbital speed. Establish a relation for orbital speed of a satellite orbiting very

close to the surface of the earth. Find the ratio of this orbital speed and escape speed.

7. What are geostationary satellites? Calculate the height of the orbit above the surface of the

earth in which a satellite, if placed, will appear stationary.

8. State Kepler's law of planetary motion.

9. What is a polar satellite? Explain how does it scan the entire earth in its each revolution? Give

two important uses of a polar. Satellite.

10. What do you mean by the term weightlessness? Explain the state of weightlessness of (i) a freely falling body (ii) an astronaut in a satellite orbiting the earth.

11. Obtain an expression for the acceleration due to gravity on the surface of the earth in terms of mass of the earth and its radius. Discuss the variation of acceleration due to gravity with

altitude and depth.

12. State the conditions necessary for a satellite to appear stationary.

^{4}km then find the angular speed of 'B' with respect to A ?when an apple falls towards the earth ,the earth ,moves up to meet the apple . WHY?

if radius of earth contracted by 0.1%, its mass remaining same, then weight of the body at earth's surface will increase by

a 0.1%

b 0.2%

c 0.3%

d Remains same

with reason

Radius of the earth is 6.4 x 10

^{6}m and mean density is 5.5 x 10^{3}kg/m^{3}. Find out the gravitational potential at the earth;s surface.what is the work done by earth's gravitaitonal force in keeping the moon in the orbit?

derive an expression for orbital velocity of a satellite.

What are the factors affecting value of G .

How much below the surface of earth dos the acceleration due to gravity become 1% of it's value at it's earth surface?

A man can jump 1.5 m high on the earth. Calculate the approximate height he might be able to jump on a planet whose density is one-quarter of the earth and the radius is one-third of the earthâ€™s radius.

what is the difference between kgf and kg wt

The gravitationalforce experienced by another 1kg mass placed at R, where OR=L.

If the radius of Earth shrinks by 1.5%, mass remaining the same, then how would the value of acceleration due to gravity change?

The escape velocity (v ) of a body depends upon the mass (m) of body, gravitational

acceleration (g) and radius(R) of the planet .Derive the relation for escape velocity

dimensionally.

how much below the surface of earth does the acceleration due to gravity

a) reduce to 36%

b)reduces by 36% of its value on the surface of earth.

Draw graphs of showing the variation acceleration due to gravity with

Show graphically how the acceleration due to gravity varies as we move from centre of earth to a great height above the surface.

18.Ans.7.08 km ${s}^{-1}$, 118 minutes.weight of a body decreases by 1.5%, when it is raised to a height h above the surface of earth. when the same body is taken to same depth h in a mine, its weeight will show

a 0.75% increase

b 0.75% decrease

c 3.0% decrease

d 1.5% decrease

Four particles A,B,C and D each of mass m are kept at the corners of a square of side L. Now the particle D is taken to infinity by an external agent keeping the other particles fixed at their respective positions. The work done by the gravitational force acting on the particle during its movement is....?a) 0

b) -GM/2R

C) -3GM/2R

D) 3GM/2R

Two uniform solid spheres of equal radii R, but mass M & 4M have a centre to centre separation 6R. The two spheres are held fixed. A projectile of mass m is projected frm the surface of the sphere of mass M directly towrds the centre of the second sphere. Obtain an expression for the minimum speed v of the projectile so that it reaches the surface of the second sphere.

(diagram of que. is given in the textbook eg.8.4 pg 193)

At what height above earth's surface, value of g is same as in a mine 100km deep?

Mention at least three conditions under which weight of a person can become zero.

differentiate geostationary satellite and polar satellite .

how many times faster than its present speed the earth should rotate so that the apparent weight of an object at equator becomes zero? Given radius of earth =6.37*106m. what would be the duration of the day in that case?

Earth is continuously pulling the moon towards the centre, still it does not fall to the Earth. Why?

The escape speed of a projectile on the earth’s surface is 11.2 km s

^{–1}. A body is projected out with thrice this speed. What is the speed of the body far away from the earth? Ignore the presence of the sun and other planets.a spherical massof 20kg lying on the earth's surface is attracted by another spherical mass of 250kg with a force equal to the weight of 0.25mg wt.the centers of the two masses are 30cm apart. calculate.the mass oeartf earth.radius of earth 6000km.

An object of mass m is raised from the surface of the earth to a height equal to the radius of the earth, that is taken from R to 2R from the centre of the earth. What is the gain in potential energy?

(I) 48 N (II) 36 N (III) 16 N (IV) 9 N

if the earth expands to twice its radius,what will be the duration of a day ?explain please

find the pecentage decease in the weight of the body when it is taken 16 km below the surface of earth

_{1}and r_{2}respectively. The time period of the planet is proportional to:-a) r

_{1}^{3}^{/2}b) r

_{2}^{3}^{/2}c) (r

_{1}+ r_{2})^{3/2}d) (r

_{1}- r_{2})^{3/2 Kindly answer sir/mam.}Find the potential energy of system of 4 particles each of mass 'm' placed at the vertices of square of side 's' also obtain the potential energy at the centre of the square.

Please explain the answer and the method of this answer

what is escape velocity?obtain the expression for the escape velocity on earth ?find escape velocity on the surface of the earth.

At what height above the earth surface does the force of gravity decreases by 1%.(radius of earth =6400km)

two point objects of mass 2x and 3x are separated by a distance r . keeping the distance fixed how much mass should be transferred from 3x to 2x so gravitaional force between them becomes maximum

State and prove kepler's third law of planetary motion by assuming the orbit to be circular

Briefly explain the principle of launching an artificial satellite. Explain the

If the acceleration due to gravity at the surface of the earth is g ,the work done in slowly lifting a body of mass m from the earths surface to a height R equal to the radius of the earth is.

a)1/2mgr

b)2mgr

c)mgr

d)none of these

A space vehicle of mass m is in a circular orbit of radius 2R

_{e}about the earth (mass m_{e}). What is the work done by an external agent to transfer it to an orbit of radius 4R_{e}.The following are my doubts:

1. Show that angular momentum of a satellite of mass M

_{s}, revolving around the earth of mass M_{e}in an orbit of radius, R is (GM_{s}^{2}M_{e}R)^{1/2}.2. Wind is blowing west to east along two parallel tracks. Two trains are moving with the same speed in opposite directions along the parallel tracks. If the relative velocity of one is double the other, what is the speed of each train?

Thanks.

A 400 KG SATELLITE IS IN A CIRCULAR ORBIT OF RADIUS 2Re ABOUT THE EARTH. HOW MUCH ENERGY IS REQUIRED TO TRANSFER IT TO A CIRCULAR ORBIT AF RADIUS 4Re ? what are the changes in the kinetic energy and potential energyif A=12.0+0.1cm and B=(8.5+0.5)cm,find(1) A+B (2)A-B