Respuesta :
Answer:
[tex]-2.0213\times 10^{-7}GMm\text{ J}[/tex]
Step-by-step explanation:
Since, the force of gravity is,
[tex]F = -\frac{GMm}{r^2}[/tex]
Where,
G = gravitational constant,
M = mass of earth,
m = mass of the particle,
r = distance of particle from centre of the earth,
∵ 7500 km = [tex]7.5\times 10^6[/tex] meters
9400 km = [tex]9.4\times 10^6[/tex] meters
Thus, work done by the force of gravity,
[tex]W=\int_{7.5\times 10^6}^{9.4\times 10^6}F. dr[/tex]
[tex]=-\int_{7.5\times 10^6}^{9.4\times 10^6}\frac{GMm}{r^2}dr[/tex]
[tex]=GMm[\frac{1}{r}]_{7.5\times 10^6}^{9.4\times 10^6}[/tex]
[tex]=GMm(\frac{1}{9.4\times 10^6}-\frac{1}{7.5\times 10^6})[/tex]
[tex]=GMm(\frac{7.5-9.4}{9.4\times 10^6})[/tex]
[tex]=-GMm(\frac{1.9}{9.4\times 10^6})[/tex]
[tex]\approx -2.0213\times 10^{-7}GMm\text{ J}[/tex]
Where,
[tex]G = 6.67408\times 10^{-11} \text{ }m^3 kg^{-1} s^{-2}[/tex]
[tex]M=5.972\times 10^24 \text{ kg}[/tex]
