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Question

A ship steams at speed v along the equator. Show that the apparent weight w of an object as weighed on the ship is given approximately by w=w0(1±4πfv/g), where f is the frequency of rotation (revolutions / second ) of the earth. Why is there a± sing ? Let w0 be the measured weight of the object when the ship is at rest relative to the earth.

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Solution

Apparent weight of any object on any moving object is given by
W=maeff where aeff is effective acceleration experienced by body.
when ship is at rest , aeff is given by gω2R
so Wo=m(gω2R)
when ship is moving with velocity v , aeff is given by gω2aR
where ωa=v/R±ω
± sign is because, it is not defined that in which direction ship is moving.
so W=m(gω2aR)
W=m(g(vR+ω)2R)

diving both equation we get
WWo=1±2vω/g
putting ω=2πf

WWo=1±4πfv/g

W=Wo(1±4πfv/g)


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