Question

Consider a solid, rigid spherical shell with a thickness of 100 m and a density of 3900 kg/m³. The sphere is centered around the sun so that its inner surface is at a distance of 1.50×10¹¹ m from the center of the sun. What is the net gravitational force Fout on a unit mass located on the outer surface of the Dyson sphere described in part a? A) 6.67 × 10⁻¹¹ N B) 9.81 N C) 2.45 × 10¹⁶ N D) 1.21 × 10²⁴ N

Answer 1

The net gravitational force on a unit mass located on the outer surface of the Dyson sphere is 2.45 × 10¹⁶ N.

Step-by-step explanation:

The net gravitational force Fout on a unit mass located on the outer surface of the Dyson sphere can be calculated using Newton's law of gravitation. The formula is given by:

Fout = (GMm) / (r²)

Where G is the gravitational constant, M is the mass of the sun, m is the mass of the unit mass, and r is the distance between the center of the sun and the outer surface of the Dyson sphere.

Substituting the given values into the formula, we can solve for the net gravitational force:

Fout = (6.674 × 10⁻¹¹ N·m²/kg²)(1.99 × 10³⁰ kg) / (1.50 × 10¹¹ m)²

= 2.45 × 10¹⁶ N

The net gravitational force on a unit mass located on the outer surface of the Dyson sphere is 2.45 × 10¹⁶ N.