Q. 285.0( 2 Votes )
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.
(a) When the ship's stationary, the speed of the ship is equal to earth's rotation. So it’s speed is .
(b) The tension in the string at the equator is given by
Where, is the earth's attraction on the bob. The difference between T0 and the earth’s attraction on the bob is
(c) The angular speed of the ship is v/R about its center. This is in the opposite direction to the earth's rotation. Hence total angular speed,
Now, tension is given by ,
Now, is a very small quantity, hence
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