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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

An earth satellite in a circular orbit at a height of 200km above the earth's surface has a period of 80 minutes. calculate the mass of the earth from this data. Radius of the earth=6400km.

Imagine a tunnel dug along a diameter of the earth.Show that a particle dropped from one end of the tunnel executes simple harmonic motion.What is the time period of this motion?

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

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

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

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.

differentiate geostationary satellite and polar satellite .

^{2}g/ω^{2})^{1/3}.what is stokes law ? What is terminal velocity?

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 .....?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.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 ?Draw graphs of showing the variation acceleration due to gravity with

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

a) 0

b) -GM/2R

C) -3GM/2R

D) 3GM/2R

derive an expression for orbital velocity of a satellite.

briefly explain the geometric meaning of angular momentum . Hence deduce Kepler's second law of planetary motion.

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

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.

An earth satellite in a circular orbit at a height of 200 km above the earth's surface has a period of 80 minutes. Calculate the mass of the earth from this data. Radius of the earth=6400 km

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

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 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 energyTwo 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)

1.) Why do different planets have different escape speeds?

2.) From where does a satellite revolving around the planet get the required centripetal force?

3.)Will 1kg of sugar be more at poles or at the equator?

4.)The centripetal force on a satellite revolving around the earth is "F" .What is the gravitational force due to earth on it and what is the net force?

CAN ANYONE SOLVE THIS QUESTIONS?

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

4.A system consists of n identical particles of mass m placed rigidly on the vertices of a regular polygon with each side of length a. If K_{1}be the kinetic energy imparted to one of the particles so that it just escapes the gravitational pull of the system and thereafter kinetic energy K_{2}is given to the adjacent particle to escape, then the difference $\left({K}_{1}-{K}_{2}\right)$ is$\left(A\right)\frac{nG{m}^{2}}{a}\left(B\right)\frac{G{m}^{2}}{na}\phantom{\rule{0ex}{0ex}}\left(C\right)\left(\frac{n}{n+1}\right)\frac{G{m}^{2}}{a}\left(D\right)\frac{G{m}^{2}}{a}$

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.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

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.

what is the moment of inertia of a sphere of mass 20 kg and radius 1/4m about its diameter?

18.Ans.7.08 km ${s}^{-1}$, 118 minutes.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

Q. Two point masses having mass m and 4m placed at distance r. The gravitational potential at a point, where gravitational field intensity zero is

$1.\frac{-9GM}{r}\phantom{\rule{0ex}{0ex}}2.\frac{-2GM}{3r}\phantom{\rule{0ex}{0ex}}3.\frac{-3GM}{r}\phantom{\rule{0ex}{0ex}}4.\frac{-6GM}{5r}\phantom{\rule{0ex}{0ex}}$

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

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

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

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

An artificial satellite of mass 1000 kg revolves around the earth in circular orbit of radius 6500Km.Calculate(a) Orbital velocity. (b) Orbital Kinetic energy (c) Gravitational potential energy. (d) Total energy in the orbit.Experts..plz help

NO LINKS PLZZ..

suppose a cyclist is negotiating a curve of radius r with speed v. write the conditions under which skidding will occur.

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}.TWO MASSES OF 800KG AND 600 KG ARE AT A DISTANCE 0.25M APART. COMPUTE THE MAGNITUDE OF INTENSITY OF GRAVITATIONAL FIELD AT A POINT DISTANCE 0.20M FROM 800KG MAS AND 0.15 M RFOM 600KG MASS.

a boat is likely to capsize if the person in the boat stands up why?