A person of mass m measures their weight with a scale. How does the person\'s we

Question

A person of mass m measures their weight with a scale. How does the person's weight measurement at the equator, W_EQ, compare with their weight measurement at the south pole, W_sp? Let T be the duration of one day. Assume the force acting on the person due to gravity has magnitude mg at both the south polo and the equator and that the Earth is a sphere of radius R. W_EQ/W_SP=1+4pi^2R/T^2g. W_EQ/W_SP= 4pi^2/t^2Rg. W_EQ/W_SP= -4pi^2/T^2Rg. W_EQ/W_SP= 1-4pi^2/T^2Rg. W_EQ/W_SP= -4pi^2R/T^2g. W_EQ/W_SP= 1+4pi^2/T^2Rg. W_EQ/W_SP= -4pi^2R/T^2g. W_EQ/W_SP= 1-4pi^2R/T^2g.

Explanation / Answer

option 8 is the correct answer.

Wsp = m*g

and

Weq = m*(g - a)

= m*(g - R*w^2) (here R is the radius of the earth and w is angular speed of the earth)

= m*(g - R*(2*pi/T)^2)

= m*(g - 4*pi^2*R/T^2)
so,

Weq/Wsp = m*(g - 4*pi^2*R/T^2)/(m*g)

= 1 - 4*pi^2*R/(T^2*g)

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