Answer:
The weight at a distance 4R from the center of earth is 10.37 N.
Explanation:
Given that,
Weight = 166 N
Distance = 4R
Let m be the mass of the object.
We know that,
Mass of earth [tex]M_{e}=5.98\times10^{24}\ kg[/tex]
Gravitational constant[tex]G = 6.67\times10^{-11}\ N-m^2/kg^2[/tex]
Radius of earth [tex]R = 6.38\times10^{6}\ m[/tex]
We need to calculate the weight at a distance 4 R from the center of earth
Using formula of gravitational force
[tex]W = \dfrac{GmM_{e}}{R^2}[/tex]
Put the value in to the formula
[tex]166=\dfrac{6.67\times10^{-11}\times m\times5.98\times10^{24}}{(6.38\times10^{6})^2}[/tex]
[tex]m=\dfrac{166\times(6.38\times10^{6})^2}{6.67\times10^{-11}\times5.98\times10^{24}}[/tex]
[tex]m=16.94 kg[/tex]
Now, Again using formula of gravitational
[tex]W=\dfrac{6.67\times10^{-11}\times 16.94\times5.98\times10^{24}}{(4\times6.38\times10^{6})^2}[/tex]
[tex]W=10.37 N[/tex]
Hence, The weight at a distance 4R from the center of earth is 10.37 N.
