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

What is the ratio of force of attraction between the two bodies kept in air and the same distance in water?

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

mass 7.2 kgis launched from the surface of the earth to acircular orbit at a height of 350 km from the surface. In doing so, find thechange in mechanical energyof the ball.(Please explain properly)

What will be the value of g at the bottom of a sea 7km deep? Radius of Earth is 6400km and g value on the surface is 9.8 m/s

^{2}.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.

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?

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.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.

$\left(1\right)\frac{x}{2\sqrt{2}}hrs\phantom{\rule{0ex}{0ex}}\left(2\right)\frac{x}{\sqrt{2}}hrs\phantom{\rule{0ex}{0ex}}\left(3\right)\sqrt{2}xhrs\phantom{\rule{0ex}{0ex}}\left(4\right)\frac{x}{2}hrs$

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

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}mderive an expression for orbital velocity of a satellite.

_{o}+alpha*t_{o}*t+1/2 alpha*t^{2}^{2}-w_{o}^{2}=2 alpha*thetaA 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 earth’s radius.

^{5}km. What is the orbital radius of a satellite that has a period of one day?what is the difference between kgf and kg wt

What is the Sense of rotation of stationary satellite around the earth ?

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

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

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.

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.

Draw graphs of showing the variation acceleration due to gravity with

if the distance between earth and sun is increased by 2% the find percentage change in gravitational force acting b/w them

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

A uniform ring of mass 10 kg and diameter 0.40mrotates with a uniform speed of 2100 rotations perminute. Find the moment of inertia and angular momentum of theringabout its geometric axisTwo 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?

_{min}=3-Ncostheta so that A does not slip during the motion of mass B. then calculate the value of NThe 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.

differentiate geostationary satellite and polar satellite .

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

Three stars of mass M and radius R are initially at rest and the distace between centres of any two stars is d and they from an equilateral triangle. They start moving towards the centroid due to mutual force of attraction. What are the velocities of the stars just before collision ?

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.^{3}from the surface of which you could barely throw a golf-ball and have it never back( Assume your best throw is 40 m/s).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?

_{0}be the orbital velocity of an artificial satellite orbiting just above the earth's surface, then the orbital velocity of the same satellite orbiting at an altitude equal to earth's radius is.$\left(1\right){v}_{0}\sqrt{\frac{2}{3}}\phantom{\rule{0ex}{0ex}}\left(2\right){v}_{0}\sqrt{\frac{3}{2}}\phantom{\rule{0ex}{0ex}}\left(3\right){v}_{0}\sqrt{2}\phantom{\rule{0ex}{0ex}}\left(4\right)\frac{{v}_{0}}{\sqrt{2}}$

Plzzz state & explain the Shell-Theorem???

force of the earth. Explain why all of them do not fall into the earth

just like an apple falling from a tree.

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

Two small particles of mass m each are placed at the vertices A and B of a right angle isoceles triangle right angled at C. If AB=l, find the gravitational field strength at C

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

If a body of mass m is taken out from a point below the surface of earth equal to half the radius of earth, R, to a height R above the earths surface, then work done on it will be

(a) (5/6) mgR

(b) (6/7) mgR

(c) (7/8) mgR

(d) (8/9) mgR

_{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.}acceleration due to gravityat surfface of planet is equal to that at surface of earth and density is 1.5 times that of earth . if radius r . then find the radius of planet

^{2}, where a is a constant. Calculate how long the satellite will remain in orbit before it falls on to the planet's surface.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

^{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}mState 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

what will be the escape speed from a planet of mass 6*10

^{16}kg and radius 3.6*10^{4}..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}.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