Q29 of 81 Page 225

The time taken by the Mars to revolve round the sun is 1.88 years. Find the ratio of average distance between Mars and the sun to that between the earth and the sun.

The period of revolution of mars is and that of earth is . Let the distance between mars and sun be and that between earth and sun be .

Now, from Kepler’s third law, the time period of an orbit is proportional to the cube of the radius of the orbit.





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27

At what rate should the earth rotate so that the apparent g at the equator becomes zero? What will be the length of the day in this situation?

 28

A pendulum having a bob of mass m is happening in a ship sailing along the equator from east to west. When the ship is stationary with respect to water the tension in the string is T0.

(a) Find the speed of the ship due to rotation of the earth about its axis.


(b) Find the difference between T0 and the earth’s attraction on the bob.


(c) If the ship sails at speed . what is the tension in the string? Angular speed of earth’s rotation is ω and radius of the earth is R.


 30

The moon takes about 27.3 days to revolve round the earth in a nearly circular orbit of radius 3.84 × 105 Km. Calculate the mass of the earth from these data.

 31

A Mars satellite moving in an orbit of radius 9.4 × 103 Km takes 27540 s to complete one revolution. Calculate the mass of Mars.