Suppose that the Sun were to collapse under its own gravitational pull. To what radius would it have to be reduced in order for the escape velocity to be equal the speed of light, 3.00 x 10⁸ m/s? The mass of the Sun is 2.00 x 10³⁰ kg and G = 6.67 x 10^-11 N·m²/kg². A) 2.96 km B) 1.48 km C) 1.52 km D) 2.10 km E) None of the other choices is correct.

Question

Quizplus · Accepted Answer

The escape velocity from the surface of an object of mass M and radius R is given by:

v = √(2GM/R)

where G is the gravitational constant.

If the escape velocity is equal to the speed of light, then:

c = √(2GM/R)

Squaring both sides and solving for R, we get:

R = 2GM/c^2

Substituting the values given in the problem, we get:

R = 2(6.67 x 10^-11 N·m^2/kg^2)(2.00 x 10^30 kg)/(3.00 x 10^8 m/s)^2

R = 2.96 km

Therefore, the Sun would have to be reduced to a radius of 2.96 km in order for its escape velocity to be equal to the speed of light. Answer choice A) is the correct choice.

Suppose That the Sun Were to Collapse Under Its Own