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?

A body is weighed by a spring balance to be 1.000 kg at the North Pole. How much will it weigh at the equator? Accounts for the earth’s rotation only.

A body stretches a spring by a particular length at the earth’s surface at equator. At what height above the South Pole will it stretch the same spring by the same length? Assume the earth to be spherical.

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 T_0.

(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.

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.