Assuming a roughly spherical shape and a density of 4000 kg/m3, estimate the diameter of an asteroid having the average mass of 1017 kg.

Respuesta :

Explanation:

It is given that,

Density of asteroid, [tex]\rho=4000\ kg/m^3[/tex]

Mass of asteroid, [tex]m=10^{17}\ kg[/tex]

We need to find the diameter of the asteroid. The formula of density is given by:

[tex]\rho=\dfrac{m}{V}[/tex]

V is the volume of spherical shaped asteroid, [tex]V=\dfrac{4}{3}\pi r^3[/tex]

[tex]r^3=\dfrac{3M}{4\pi \rho}[/tex]

[tex]r^3=\dfrac{3\times 10^{17}\ kg}{4\pi \times 4000\ kg/m^3}[/tex]

[tex]r^3=\sqrt{5.96\times 10^{12}}[/tex]

r = 2441311.12 m

Diameter = 2 × radius

d = 4882622.24 m

or

[tex]d=4.88\times 10^6\ m[/tex]

Hence, this is the required solution.

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