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The kinetic energy of the rocket is (initial):-                                                           And the initial potential energy is :                                                           Thus total initial energy is given by :                                                                Further, it is given that 20 per cent of kinetic energy is lost. So the net initial energy...
Firstly, the potential energy of spaceship due to the sun is given by :                                                                        and the potential energy of spaceship due to mars is given by :                                                                        It is given that the spaceship is stationary so its kinetic energy is zero. Thus the total energy of spaceship is :    ...
A body will get stuck at the star's surface if the centrifugal force of star is less than the gravitational force. The gravitational force is given by :                                                          or                                                              The centrifugal force is given by :                                                            or                         ...
Height of satellite from earth's surface :     Gravitational potential is given by :                                                             or                                                        or                                                        Thus potential due to earth gravity is   .
Total energy of stars is given by :                                          or                                             or                                             Now when starts are just to collide the distance between them is 2R. The total kinetic energy of both the stars is :                                                    And the total energy of both the stars is :              ...
The total energy of the satellite at height h is given by :                                                                We know that the orbital speed of the satellite is :                                                          Thus the total energy becomes :                                                      or                                                  Thus the required energy is...
Let us assume the speed of the body far away from the earth is  . Total energy on earth is :                                                  And the total energy when the body is far from the earth is :                                                                            (Since the potential energy at far from the earth is zero.) We will use conservation of energy :  -                 ...
The total energy is given by :                                       Total energy  =  Potential energy  +  Kinetic energy                                                            At the highest point velocity will be zero. Thus the total energy of the rocket is :                                                              Now we will use the conservation of energy :                          ...
Position of the body is (depth)  :                                                   Acceleration due to gravity at depth d is given by :                                               or                                                 or                                                 Thus the weight of the body is:-                                               or                             ...
Acceleration due to gravity at height h from the surface of eath is :                                          For         we have :                                                        or                                                           Thus the weight of the body will be :                                                       or                                                     ...
Kepler's third law give us the following relation :                                                               Thus we can write :                                                              or                                                        or                                                                or                                                                Thus the...
Mass of sun can be calculated by using the following formula:-                                                Putting the known values in the above formula, we obtain :                                                     or                                                 Thus the mass of the sun is nearly  .
Let the distance where the gravitational force acting on satellite P becomes zero be x from the earth. Thus we can write :                                                       or                                                  or                                                                       Hence :                                                                                       ...
As stated in the previous question, the gravitational potential in a spherical shell is constant throughout. So the gravitational intensity will act in downward direction (as upper half is cut). So the required direction is shown by arrow e.
We know that the gravitational potential (V) in a sphere is constant throughout. Also, the gravitational intensity will act in the downward direction as its upper half is cut (gravitational force will also act in a downward direction). Hence the required direction of gravitational intensity is shown by arrow C.
(a) In space we have state of weightlessness, so the swollen feet does not affect astronaut as there is no gravitational pull (so cannot stand). (b) The swollen face will be affected as the sense organs such as eyes, ears etc. will be affected. (c) It will affect the astronaut as it may cause mental strain. (d) It will affect the astronaut as space has different orientations.
Among all only angular momentum and total energy of the comet will be constant other all factors given will vary from point to point.
The escape velocity from the earth is given by :                                             Since the escape velocity depends upon the reference (potential energy), so it only depends upon the height of location. (i)   No (ii)   No (iii)  No (iv)  Yes
(a) The total energy will be negative of its kinetic energy. Since at infinity potential energy is zero and total energy is negative. (b) The energy required will be less as the stationary object on earth has no energy initially whereas the satellite has gained energy due to rotational motion.
We know that one light year is . The time period of rotation is given by :                                               Putting all the value (in SI units) in the above equation we get :                                                       or                                                   In years :
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