Question

The mass of the body on the surface of the earth is 100 kg. What will be its (i) mass and (ii) weight at an altitude of 1000 km? (R = 6400 km, g = 9.8 m / s²)

Answer 1

In order to the solution of the above numerical we should use the formula of acceleration due to gravity due to an altitude and then by using this we can calculate the weight.

Complete Step by step answer:
From the given data:
${g_0} = 9.8m{s^{ - 2}} \\\ h = 1000km \\\ R = 6400km \\\$
Firstly from the given information the mass of an earth doesn't change. It will be constant in all places or locations. Therefore the mass of the body at an altitude of 1000km should be equal to 100kg.
By using the acceleration due to gravity due to an altitude formula, we get
$g = \dfrac{{{g_0}}}{{{{\left( {1 + \dfrac{h}{R}} \right)}^2}}}$
$\Rightarrow g = \dfrac{{1000}}{{{{\left( {1 + \dfrac{{1000}}{{6400}}} \right)}^2}}} \\\ \Rightarrow g = 7.33m{s^{ - 2}} \\\$
We know that
Weight = mass × acceleration due to gravity
W=mg
$\Rightarrow W = 100 \times 7.33 \\\ \therefore W = 733N \\\$
Hence we calculated the weight at an altitude of 733N.

Note: If the altitude changes then the acceleration of an object also changes. The inverse- square law obeys when the change in acceleration due to gravity with distance from the earth. This implies that acceleration due to gravity is inversely proportional to the square of the distance from earth. If the distance doubles then the acceleration due to gravity decreases by four times.