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While weight of a body depends directly on acceleration due to gravity g, the value of g depends upon many factors. It depends on the shape of the Earth, rotation of the Earth, etc. Weight of a body at a pole is more than that at a place on equator because g is maximum at poles and minimum on equator. Acceleration due to gravity g varies with latitude lambda according to the equation g_x = g - R omega^2 cos^2lambda, where R is radius of Earth and omega is angular velocity of Earth. A body of mass m weighs W_r in a train at rest. The train then begins to run with a velocity v around the equator from west to east. It conserved that weight W_m of the same body in the moving train is different from W_r"Let "v_e be the velocity of a point on equator with respect to axis of rotation of Earth and R be the radius of the Earth. Clearly, the relative velocity between Earth and train will affect the weight of the body. Difference in the weight in the two given states

Answer»

<P>`m/Rv_e^2`
`m/R (V_e + V)^2`
`m/R [(v_e+v)^2 - v_e^2]`
`m/R p[(v_e-v)^2 - v_r^2]`

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