Answer:
Mass of the planet, [tex]M=9.59\times 10^{24}\ kg[/tex]
Explanation:
Given that,
Mass of the object, m = 0.5 kg
Weight of the object, W = 20 N
Radius of the planet, [tex]r=4\times 10^6\ m[/tex]
The weight of an object is given by :
W = mg
g is the acceleration due to gravity on the surface of Planet
[tex]g=\dfrac{W}{m}[/tex]
[tex]g=\dfrac{20}{0.5}[/tex]
[tex]g=40\ m/s^2[/tex]
The expression for g is given by :
[tex]g=\dfrac{GM}{r^2}[/tex]
[tex]M=\dfrac{r^2g}{G}[/tex]
[tex]M=\dfrac{(4\times 10^6)^2\times 40}{6.67\times 10^{-11}}[/tex]
[tex]M=9.59\times 10^{24}\ kg[/tex]
So, the mass of the planet X is [tex]9.59\times 10^{24}\ kg[/tex]. Hence, this is the required solution.
