(Solved): 2. Planet \( X \) rotates in the same manner as the earth, around an axis through its north and sou ...

2. Planet \( X \) rotates in the same manner as the earth, around an axis through its north and south poles, and is perfectly spherical. An astronaut who weighs \( 948.0 \mathrm{~N} \) on the earth weighs himself on Planet \( \mathrm{X} \) by stepping on a scale at two different locations; the scale reads \( 912.0 \mathrm{~N} \) at the north pole of Planet \( X \) and only \( 849.0 \mathrm{~N} \) at its equator. The distance from the north pole to the equator is \( 1.887 \times 10^{4} \mathrm{~km} \), measured along the surface of Planet X. a) Why does the scale give a different reading at the north pole than at the equator? b) Based on the given data, how long is a day on Planet \( \mathrm{X} \) ?