Question

If the Sun collapses into a black hole, what is the difference in the gravitational attraction on a 1.0-kg mass at the head and at the feet of an investigator 300 km from the center?

a) 6.73 x 10^5 N
b) 8.21 x 10^5 N
c) 5.42 x 10^5 N
d) 7.98 x 10^5 N

Answer 1

The difference in the gravitational attraction (tidal force) at two points can be calculated using Newton's law of universal gravitation, accounting for the difference in distance from the mass causing the gravitational field. However, without the mass of the Sun, a numeric answer cannot be provided.

Step-by-step explanation:

To find the difference in the gravitational attraction at the head and feet of an investigator 300 km from the center of a collapsed Sun into a black hole, we'll use Newton's law of universal gravitation. The formula for the gravitational force is F = GMm/r2, where G is the gravitational constant, M is the mass of the larger object, m is the mass of the smaller object, and r is the distance between the centers of the two masses.

Assuming the investigator's height is negligible compared to 300 km, the difference in force (tidal force) due to a gravitational gradient can be found using the formula ΔF = (2GMmΔr) / r3, where Δr is the difference in distance between the head and feet.

Because the student's question does not provide the mass of the Sun, we can't calculate a numeric answer. However, the conceptual approach involves calculating the gravitational force at the distance of the feet (300 km from the center) and at the head (300 km + the height of the investigator), then finding the difference between these two forces.