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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

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

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....?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.

_{P}and M_{Q}and surface areas A and 4A respectively. A spherical planet R also has uniform density p and its mass is (M_{P}+ M_{Q}). The escape velocities from the planets P, Q and R are V_{ p}, V_{Q}and V_{ R}respectively. Then1) V

_{Q }>_{ }V_{ R }>_{ }V_{ p }2) V_{R }>_{ }V_{ Q }>_{ }V_{ p}3) V

_{ R}/_{ }V_{ p }= 3 4) V p/ V_{ Q = $\frac{1}{2}$}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.

(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

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

^{4}km then find the angular speed of 'B' with respect to A ?Q.3. Two uniform spherical stars made of same material have radii R and 2R. Mass of the smaller planet is m. They start moving from rest towards each other from a large distance under mutual force of gravity. The collision between the stars is inelastic with coefficient of restitution 1/2.

(a) Find the kinetic energy of the system just after the collision.

(b) Find the maximum separation between their centres after their first collision.

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

derive an expression for orbital velocity of a satellite.

Q35. One end of a spring is fixed to the celling and other end is attached to a block. The block is released when spring is relaxed. The product of time period and amplitude is 8 S. l, units. If spring is cut in two equal parts and the two springs are attached to the block as shown in figure. The block is released when both springs are relaxed. Now find the product of time period and amplitude in S.l. units.

Q.31. A particle would take a time t to move down a straight tube from the surface of earth (supposed to be a homogeneous sphere) to its centre. If gravity were to remain constant, then the time would be t. The ratio of t/t' will be

(a) $\frac{\mathrm{\pi}}{2\sqrt{2}}$

(b) $\frac{\mathrm{\pi}}{\sqrt{2}}$

(c) $\sqrt{2}\mathrm{\pi}$

(d) $\frac{\mathrm{\pi}}{\sqrt{2}}$

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

(A)less

(B)more

(C)same

(D)nil

GIVE VALID REASON FOR YOUR ANSWER IN A WELL DETAILED MANNER!

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.

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.

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

11. The gravitational potential changes uniformly from -20 J/kg to -40 J/kg as one moves along X-axis from

x = - 1 m to x = + 1 m. Mark the correct statement about gravitational field intensity of origin.

(A) The gravitational field intensity at x = 0 must be equal to 10 N/kg

(B) The gravitational field intensity at x = 0 may be equal to 10 N/kg

(C) The gravitational field intensity at x = 0 may be greater than 10 N/kg

(D) The gravitational field intensity at x = 0 must not be less to than 10 N/kg

a) 0

b) -GM/2R

C) -3GM/2R

D) 3GM/2R

(A) $\sqrt{\frac{2\mathrm{GM}}{\mathrm{a}}}$ (B) $\sqrt{\frac{2\mathrm{GM}}{\mathrm{a}}\left(1-\frac{1}{\sqrt{2}}\right)}\phantom{\rule{0ex}{0ex}}$ (C) $\sqrt{\frac{2\mathrm{GM}}{\mathrm{a}}\left(\sqrt{2}-1\right)}$ (D) zero

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?

about its axis

differentiate geostationary satellite and polar satellite .

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

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) Particle will oscillate through the earth to a height h = R on both sides.

(2) Motion of the particle is periodic.

(3) Motion of the particle is simple harmonic.

(4) Both (1) and (2).

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

a dancer in ice spins faster when she folds her arms.This is due to?

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

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.

_{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.}^{-1}what is escape velocity?obtain the expression for the escape velocity on earth ?find escape velocity on the surface of the earth.

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

36. A satellite of mass 1000 kg moves in a circular orbit of radius 7000 km around the earth.Calculate the total energy required to place the satellite in orbit from earth's surface. Take Radius of earth = 6400 km and g =10.0

ms

^{-2.}37. An astronaut puts a ball of mass 7.2kg into a circular orbit about the earth at a height of 350 km.(i) what is the kinetic energy of the ball (ii) what is the potential energy of the ball?

38. An earth satellite makes a circular around the earth in 90 minutes. Calculate the height of satellite above theearth's surface. Radius of earth = 6400 kmand g = 9.8ms-2

39. An artificial satellite is revolving at a height of 500 km above the earth's surface in a circular orbit, completing one revolution in 98 minutes. Calculate the mass of the earth. Given, G = 6.67 x 10

^{-11}N m^{-2}kg^{-2}and R_{e}= 6.4 x 10^{6}m.40. If the period of revolution of an artificial satellite just above the earth by T and the density P, then prove that p T

^{-2}is a universal constant.Calculate the value of this constant if G = 6.67 x 10^{-11}N m^{-2}kg

^{-2}41. With what velocity must a body be thrown upward from the surface of the earth so that it reaches a height of 10 R = 6400 km. Mass of earth, M = 6 x 10

^{24}kg and G=6.67 x 10

^{-11}N m^{2}kg^{-2.}42. An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escapevelocity from the earth (i) Determine the height of satellite above the earth's surface. (ii) If the satellite is stopped suddenly in its orbit and allowed to fall freely into the earth, find the speed with which it hits the surface of the earth. Take g = 9.8 m s

^{-2}and R_{e}= 6400 km.43. An artificial satellite of mass 200 kg revolves around the earth in an orbit of average radius 6670 km. Calculate its orbital K.E., the gravitational potential energy and the total energy = 6.0 x 10

^{24}kg and G = 6.67 x 10^{-11}N m^{2}kg-2.44. If the distance of the planet jupiterfrom the sun is 5.2 times that of the earth, calculate the period of jupiter's revolution around the sun.

45.The ratio of thetimeperiods of revolution of mars and earth around the sun is 1.88. Find the ratio of the distances of these planets from the sun.

46.Moon describes a circular orbit of radius 4 x 10

^{8}m around the earth in 28 days. Titan desctribes a circular orbit of radius 1.6 x 10^{9}in around the saturn in 16 days. Compare the masses of saturn and the earth.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

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

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}.1. A block of mass m is stationary with respect to a rough wedge as shown in figure. Starting from rest, in time t work done on the block : (m = 1 kg, θ = 30°, a = 2 m/s2 t = 4s)

Column I Column II

(A) By gravity (p) 144 J

(B) By normal reaction (q) 32 J

(C) By friction (r) 56 J

(D) By all the forces (s) 48 J

(t) None

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