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Question

A pendulum having a bob of mass m is hanging 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 atraction on the bob (c) If the ship sails at speed v, what is the tension in the string? Angular speed of earth's rotaton is ω
and radius of the earth is R.

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Solution

Speed of the ship due to rotation of earth
v=ωR.
(b) T0=mgmω2Rt0mg=mω2R
(c) IF the ship shifts at speed 'v'
T=mgmω21R=T0(vωR)2R2R=T0(v2+ω2R22ωRv)RRT=T0+2ωvm


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