Answer:
The mass of mars is [tex]6.61\times10^{23}\ kg[/tex]
Explanation:
Given that,
Time = 1.02 s
Height = 2.00 m
Radius of mars [tex]r= 3.39\times10^{6}\ m[/tex]
We need to calculate the acceleration due to gravity on mars
Using equation of motion
[tex]h = ut+\dfrac{1}{2}gt^2[/tex]
[tex]h = \dfrac{1}{2}gt^2[/tex]
[tex]g=\dfrac{2h}{t^2}[/tex]
Where, u = initial velocity
t = time
h = height
Put the value into the formula
[tex]g=\dfrac{2\times2.00}{(1.02)^2}[/tex]
[tex]g=3.84\ m/s^2[/tex]
We need to calculate the mass of mars
Using formula of gravity
[tex]g=\dfrac{Gm}{r^2}[/tex]
Put the value into the formula
[tex]3.84=\dfrac{6.67\times10^{-11}\times m}{(3.39\times10^{6})^2}[/tex]
[tex]m=\dfrac{3.84\times(3.39\times10^{6})^2}{6.67\times10^{-11}}[/tex]
[tex]m=6.61\times10^{23}\ kg[/tex]
Hence, The mass of mars is [tex]6.61\times10^{23}\ kg[/tex]
