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 $T_{0}$ (a) Find the speed of the ship due to rotation of the earth about its axis. (b) find the difference between $T_{0}$ 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
$v = ω R .$
(b) $T_{0} = m g - m ω^{2} R ∴ t_{0} - m g = m ω^{2} R$
(c) IF the ship shifts at speed 'v'
$T = m g - m ω_{1}^{2} R = T_{0} - \frac{(v - ω R)^{2}}{R^{2}} R = T_{0} - \frac{(v^{2} + ω^{2} R^{2} - 2 ω R v)}{R} R ∴ T = T_{0} + 2 ω v m$

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Speed of the ship due to rotation of earth v=ωR. (b) T0=mg−mω2R∴t0−mg=mω2R (c) IF the ship shifts at speed 'v' T=mg−mω21R=T0−(v−ωR)2R2R=T0−(v2+ω2R2−2ωRv)RR∴T=T0+2ωvm