A planet is made of two distinct materials in two layers.From the core to R/2,the density of the material is 4000 kg/m³,and from R/2 to R the density is 3000 kg/m³.What is the mass of the planet if R = 5000 km? A)2.62 $\times$ 10²³ kg B)1.37 $\times$ 10²⁴ kg C)1.64 $\times$ 10²⁴ kg D)1.57 $\times$ 10²⁴ kg E)1.87 $\times$ 10²⁴ kg

Question

Quizplus · Accepted Answer

We can use the formula for the mass of a planet with two distinct materials in two layers:

$M = \frac{4}{3}\pi R^3 (ho_1 \frac{R}{2}+ho_2 \frac{R}{2})$

Plugging in the given values, we get:

$M = \frac{4}{3}\pi (5000 	ext{ km})^3 (4000 	ext{ kg/m}^3 \frac{5000	ext{ km}}{2} + 3000 	ext{ kg/m}^3 \frac{5000	ext{ km}}{2})$

Simplifying and converting units, we get:

$M = 1.64 	imes 10^{24} 	ext{ kg}$

Therefore, the answer is (C).

A Planet Is Made of Two Distinct Materials in Two ×\times×

A Planet Is Made of Two Distinct Materials in Two $\times$