Answer: The weight of the person above the surface of a planet is 635.83N.
Explanation:
To calculate the weight of a person, we use the formula:
\(w=mg\) ....(1)
where,
w = weight of an object
m = mass of the person = 65kg
g = acceleration due to the gravity of the planet
For the calculation of weight, we need to first find the acceleration due to gravity and for that we use the formula:
\(g=\frac{GM}{r^2}\)
where, g = acceleration due to gravity = \(?m/s^2\)
G = Universal gravitational constant = \(6.67\times 10^{-11}Nm^2/kg^2\)
M = mass of the planet = \(5.97\times 10^{24}kg\)
r = distance of the person from the planet = \(6.38\times 10^6m\)
Putting values in above equation, we get:
\(g=\frac{(6.67\times 10^{-11}kgm/s^2.m^2/kg^2)(5.97\times 10^{24}kg)}{(6.38\times 10^6m)^2}\\\\g=9.782m/s^2\)
Putting this value in equation 1, we get:
\(w=65kg\times 9.782m/s^2=635.83N\)
Hence, the weight of the person above the surface of a planet is 635.83N.