Question

Mars has a mass of 6.42×1023 kg and a radius of 3.40×106 m. Assume a person is standing on a bathroom scale on the surface of Mars. Part A Over what time interval would Mars have to complete one rotation on its axis to make the bathroom scale have a zero reading? Express your answer with the appropriate units.

Answer 1

Answer:

T = 1.67 hours

Explanation:

It is given that,

Mass of mars, $M=6.42\times 10^{23}\ kg$

Radius of mars, $r=3.4\times 10^{6}\ m$  

Let m is the mass of the person standing on a bathroom scale on the surface of Mars. As the person rotates on its axis, the force of gravitation is balanced by the centripetal force as:

$m\omega^2 r=\dfrac{GmM}{r^2}$

$\omega^2 r=\dfrac{GM}{r^2}$

Since, $\omega=\dfrac{2\pi}{T}$

$(\dfrac{2\pi}{T})^2 r=\dfrac{GM}{r^2}$

$T^2=\dfrac{4\pi ^2r^3}{GM}$

$T^2=\dfrac{4\pi ^2\times (3.4\times 10^{6})^3}{6.67\times 10^{-11}\times 6.42\times 10^{23}}$

T = 6019.60 seconds

or

T = 1.67 hours

So, the time taken is 1.67 hours. Hence, this is the required solution.