The value of g at the surface of the spherical Asteroid X is 0.0060 m/s² and the escape velocity is 10.1 m/s.What is the mass of this asteroid? (G = 6.67 × 10^-11 N ∙ m²/kg²) A)2.3 × $10^{16}$ kg B)3.5 × $10^{12}$ kg C)6.5 × $10^{15}$ kg D)4.9 × $10^{14}$ kg E)6.7 × $10^{13}$ kg

Question

Quizplus · Accepted Answer

The formula for the escape velocity of an object is:

v_esc = √(2GM/r)

where v_esc is the escape velocity, G is the gravitational constant, M is the mass of the object, and r is the radius of the object.

We can rearrange this formula to solve for the mass M:

M = (v_esc^2 * r) / (2G)

Plugging in the given values, we get:

M = (10.1^2 * 1) / (2 * 6.67 × 10^-11 * 0.0060)

M = 6.5 × 10^15 kg

Therefore, the best choice is C.

The Value of G at the Surface of the Spherical 101610^{16}1016

The Value of G at the Surface of the Spherical $10^{16}$