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Syllabus

state and prove work-energy theorem.

Establish a relationship between g and G.

when an apple falls towards the earth ,the earth ,moves up to meet the apple . WHY?

relation between escape velocity and orbital velocity

## If the earth has a mass 9 times and radius twice of a planet Mars calculate the minimum velocity required by a rocket to pull out of gravitational force of mars. Take the escape velocity on the surface of earth to be 11.2 km/s

(1) Move around planet in circular orbit

(2) Move around planet in elliptical orbit

(3) Escape out with minimum speed

(4) Escape out with speed greater than escape velocity

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

Q1 . if earth has a mass 9 times and radius 2 times that of mars , calculate the minimum speed required by a rocket to pull out of gravitational force of mars .take the escape speed on the surface of earth to be 11.2 km/s

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

^{4}km then find the angular speed of 'B' with respect to A ?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.

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}.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

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.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.

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 .....?$\left(1\right)\sqrt{\frac{3GM}{4R}}\phantom{\rule{0ex}{0ex}}\left(2\right)\sqrt{\frac{2GM}{3R}}\phantom{\rule{0ex}{0ex}}\left(3\right)\sqrt{\frac{GM}{2R}}\phantom{\rule{0ex}{0ex}}\left(4\right)\sqrt{\frac{2GM}{R}}$

particle of mass m_{1 }liesinside aat aspherical shellof mass m_{2 }and radius Rdistance of r from the centre. Find thegravitational potential energy of the system.(Please explain properly and the answer given is (-Gm

_{1}m_{2})/R.)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

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 10 kg mass is to be divided into two parts such that the force of attraction between them is maximum.What is the mass of each portion?

derive an expression for orbital velocity of a satellite.

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

D)may be positive ,negative or zero..

plsgiv the crt ans and plz explain it ,thank u

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

What are the factors affecting value of G .

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.

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)

_{0}. The potential at a point distance half the radius of earth from the centre will be.$\left(1\right)\frac{11}{4}{V}_{0}\phantom{\rule{0ex}{0ex}}\left(2\right)\frac{{V}_{0}}{2}\phantom{\rule{0ex}{0ex}}\left(3\right)2{V}_{0}\phantom{\rule{0ex}{0ex}}\left(4\right)\frac{11}{8}{V}_{0}$

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

_{e}= 6400 Km).(1) 6400 Km

(2) 57600 Km

(3) 2560 Km

(4) 6400 Km

what are the conclusions of newton's law from kepler's law???????

differentiate geostationary satellite and polar satellite .

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

what is the maximum value gravitational potential and where??

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.47.At what height from the surface of earth, the total energy of satellite is equal to its potential energy at a height 2R from the surface of earth (R=radius of earth)-------

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?

A particle of mass 50g is kept on the surface of uniform sphere of mass 120kg and radius 50cm.Find the work to be done against the gravitational force between them to take the particle far away from the sphere.An artificial satellite is moving in a circular orbit around earth with a speed equal to half the magnitude of escape velocity from earth .1. Determine the hieght of the satellite above the earth's surface2.If the satellite is topped suddenly in its orbit and allowed to fall freely towards the earth, find the speed with which it hits the surface of the earth.

how is GM=gR^2?

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

kinetic/potential energy.

Answer:

(a) Kinetic energy

(a) Total mechanical energy of a satellite is the sum of its kinetic energy (always positive) and potential

energy (may be negative). At infinity, the gravitational potential energy of the satellite is zero. As the

Earthsatellite system is a bound system, the total energy of the satellite is negative.

Thus, the total energy of an orbiting satellite at infinity is equal to the negative of its kinetic energy.

please explain this in a better way ,may be diagrammatically. i did not understood this answer.1. 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.

halley's comet has a period of 76 years and in 1986 had a distance of closest approach to the sun equal to 8.9*10^{10}m.the comets farthest distance from the sun is the mass of the sun is 2*10^{30}kg in MKSunits.a)2.7*10^{12}mb(2.7*10^{13}mc)5.3*10^{12}md)5.3*10^{13}mwhat is escape velocity?obtain the expression for the escape velocity on earth ?find escape velocity on the surface of the 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.}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

what does central force mean?

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 body weighs 300 N on the earth's surface. what is its weight at a depth of 1/3rd of radius of earth?

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 energy