Answer:
7160.2812 s or 1.988 hours
Explanation:
m = Mass of person
R = Radius of Earth = [tex]6.37\times 10^{6}\ m[/tex]
g = Acceleration due to gravity = 9.81 m/s²
[tex]\omega[/tex] = Angular speed
Force at equator would be
[tex]F_e=m(g-\omega^2R)[/tex]
Force at pole
[tex]F_p=mg[/tex]
From the question
[tex]F_e=\dfrac{1}{2}F_p\\\Rightarrow m(g-\omega^2R)=\dfrac{1}{2}F_p\\\Rightarrow \omega=\sqrt{\dfrac{g}{2R}}[/tex]
Time period is given by
[tex]T=\dfrac{2\pi}{\omega}\\\Rightarrow T=2\pi\sqrt{\dfrac{2R}{g}}\\\Rightarrow T=2\pi\sqrt{\dfrac{2\times 6.37\times 10^6}{9.81}}\\\Rightarrow T=7160.2812\ s=1.988\ hours[/tex]
The rotational period of the planet is 7160.2812 s or 1.988 hours
