Answer:
The mass of the planet is [tex]M=2.5*10^{25}kg[/tex]
Explanation:
We have a first part of the problem, which we resolve with kinematics, knowing that
[tex]d=d_{0}+v_{0}t+\frac{1}{2}at^2[/tex]
where d is given (5.50m), d₀ is zero, v₀ is zero too (as the wrench starts falling from static position), t is given (0.811s), and a is what we want to know for the second part of the problem. We clear a
[tex]a=\frac{2*5.5m}{(0.811s)^2}=16.72\frac{m}{s^2}[/tex]
Then for the second part, we use Newton's gravitational Law, where
[tex]F_{g}=G\frac{mM}{r^2}[/tex]
m is the wrench mass, M is the planet mass, G is the gravity universal constant, and r is calculated from the given circumference (with the correct units) as
[tex]2\pi r=6.28*10^7m\Leftrightarrow r=\frac{6.28*10^7m}{2\pi}=9994930.4m[/tex]
Finally, we have that
[tex]F_{g}=G\frac{mM}{r^2}\Leftrightarrow ma=G\frac{mM}{r^2}\Leftrightarrow a=G\frac{M}{r^2}\Leftrightarrow M=\frac{ar^2}{G}[/tex]
Therefore, replacing with the data calculated, and the known value of G, we can calculate M of the planet
[tex]M=\frac{16.72*9994930.4^2}{6.67428*10^{-11}}=2.5*10^{25}kg[/tex]
