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A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 1000 kg. It has strayed too close to a black hole having a mass 100 times that of the Sun. The nose of the spacecraft points toward the black hole, and the distance between the nose and the center of the black hole is 10.0 km.

(b) What is the difference in the gravitational fields acting on the occupants in the nose of the ship and on those in the rear of the ship, farthest from the black hole?

(Note: This difference in accelerations grows rapidly as the ship approaches the black hole. It puts the body of the ship under extreme tension and eventually tears it apart.)

Answer :

The difference in the gravitational fields acting on the occupants in the nose of the ship and on those in the rear of the ship, farthest from the black hole can be calculated using the equation for gravitational field strength:
g = (G * M) / r^2

Where g is the gravitational field strength, G is the gravitational constant, M is the mass of the black hole, and r is the distance between the occupants and the center of the black hole. Since the mass of the black hole is 100 times that of the Sun, we can assume it to be approximately 1.989 x 10^31 kg.

The distance between the nose of the spacecraft and the center of the black hole is given as 10.0 km, which can be converted to 10,000 m. Plugging these values into the equation, we can calculate the gravitational field strength at the nose of the ship and at the rear of the ship. The difference between these two values will give us the difference in gravitational fields acting on the occupants. Note that as the ship approaches the black hole, this difference in accelerations will increase rapidly, eventually tearing the ship apart due to extreme tension.

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