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Syllabus

state and prove work-energy theorem.

a) 0

b) -GM/2R

C) -3GM/2R

D) 3GM/2R

Establish a relationship between g and G.

relation between escape velocity and orbital 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 .....?if earth were suddenly shrink to half of its present radius without change in mass,what is the effect on duration of days?

^{2})ā (1) 6.5 km/sā (2) 8 km/s

(3) 10 km/s (4) 11.2 km/s

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

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

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.

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

^{6}m above the surface of the Earth. If Earth's radius is 6.38 × 10^{6}m and g = 9.8 m/s^{2}^{ }then the orbital speed of the satellite is(a) 5.86 km/s (b) 9.13 km/s (c) 6.67 km/s (d) 7.76 km/s

if all objects on the equator feels weightlessness then duration of the day will become___

what is stokes law ? What is terminal velocity?

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....?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 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.^{4}km then find the angular speed of 'B' with respect to A ?_{0}, its maximum speed will be:-a) v

_{0}R/rb) v

_{0}r/Rc) v

_{0}R^{2}/r^{2}d) v

_{0}r^{2}/R^{2}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

derive an expression for orbital velocity of a satellite.

(1) Fall back on surface of earth by following parabolic path

(2) Fall back on surface of earth by following hyperbolic path

(3) Start rotating around earth in a circular orbit

(4) Escape from gravitational field of earth

what is the difference between kgf and kg wt

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 earthās radius.

Q. What is the ratio of the kinetic energy required to be given to the satellite to escape earth's gravitational field to the kinetic energy required to be given so that the satellite moves in a circular orbit just above earth's atmosphere?

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.

^{2}g/ω^{2})^{1/3}.If the radius of Earth shrinks by 1.5%, mass remaining the same, then how would the value of acceleration due to gravity change?

If potential energy of a body of mass m on the surface of earth is taken as zero then its potential energy at height h above the surface of earth is (R is radius of earth and M is the mass of earth)

a)-GMm/(R+h)

b)-GMm/(h)

c)GMmh/R(R+h)

d)GMmh/(h+2R)

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.

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

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

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

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?

a)3/4 times of earth

b) 3 times of earth

differentiate geostationary satellite and polar satellite .

_{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.}The ratio of kinetic energy of a planet at perigee and apogee during its motion around yhe sun in elliptical orbit of eccentricity is what?

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?

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.

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

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

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

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

the mean radius of the earth's orbit round the sun is 1.5x10 to power11. the mean radius of the orbit of mercury round the sun is 6x10to power 10 m. the mercury will around sun in how many years?

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 rocket is fired vertically with a speed of 5 km s

^{-1}from the earth's surface. How far from the earth does the rocket go before returning to the earth ? Mass of the earth = 6 x 10^{24}kg; mean radius of the earth = 6.4 x 10^{6}m; G= 6.67 x 10^{-11}N m^{2}kg^{-2}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

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?

^{-7}rad/s in a circular orbit of radius 1.5*10^{8}km. the force exerted by sun on earth isDetermine the speed wih which the earth would have to rotate on its own axis so that a person on the equator would weight 3/5th as much as present?

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

If radius of earth were increased by a factor of 3, by what factor would its density have to be changed to keep the value of āgā same.