Respuesta :
Answer:
2352645198509.9604 m/s²
Explanation:
G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²
M = Mass of black hole = [tex]90\times 1.989\times 10^{30}\ kg[/tex]
[tex]R_{f}[/tex] = 10000+100 m
[tex]R_{sb}[/tex] = Distance between the nose and the center of the black hole = 10000 m
The difference in the gravitational field in this system is given by
[tex]\Delta F=\dfrac{GMm}{R_{f}^2}-\dfrac{GMm}{R_{sb}^2}\\\Rightarrow \Delta g=GM\left(\frac{1}{R_f^2}-\frac{1}{R_{sb}^2}\right)\\\Rightarrow g=6.67\times 10^{-11}\times 90\times 1.989\times 10^{30}\left(\frac{1}{(10000+100)^2}-\frac{1}{10000^2}\right)\\\Rightarrow \Delta g=-2352645198509.9604\ m/s^2[/tex]
The acceleration is 2352645198509.9604 m/s²
The difference in the gravitational field acting on the occupants in the nose of the ship and on those in the rear of the ship, farthest from the black hole will be - 2.35 ×10¹⁶ m/sec.
What is the gravitational field?
An imaginary field in which the gravitational force is observed is known as the gravitational field.
The given data in the problem is;
G is the gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²
M is the Mass of the black hole = 90 ×1.989×10³⁰ Kg
[tex]R_f[/tex] is the final radius = 10000+100 m
R₁₂ is the distance between the nose and the center of the black hole=10000 m
The gravitational field is found by the difference in the gravitational force;
[tex]\rm \trianglr F= \frac{GmM}{R_f^2} - \frac{GMm}{R_{12}^2} \\\\ \triangle g = GM(\frac{1}{R_f} )^2-(\frac{1}{R_{12}} )^2 \\\\ \triangle g = 6.67 \times 10^{-11}\times 90 \times 1.989 \times 10^{30} (\frac{1}{10100} )^2-(\frac{1}{10000}} )^2 \\\\ \triangle g = -2.35 \times 10^{16}\ m/sec^2[/tex]
Hence the difference in the gravitational field is -2.35 ×10¹⁶ m/sec.
To learn more about the gravitational field refer to the link;
https://brainly.com/question/26690770
