Measuring g

A person standing on the north pole of the earth measures the acceleration due to gravity as $-9.81~m.s^2$ by resting a 1 kg block on a spring scale and measuring the force exerted by the scale. What value for the magnitude of the acceleration of gravity in $m/s^2$ would a person on the equator measure if they performed this experiment?

Details and assumptions

• You may treat the earth as a perfect sphere of radius 6370 km.
• Take the length of a day to be exactly 24 hours.