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A man on the moon with a mass of 90 kilograms weighs 146 newtons. The radius of the moon is 1.74 x 106 meters, find the mass of the moon.
a) 7.36 x 10^(28) kg
b) 2.4 x 10^(10) kg
c) 7.36 x 10^(22) kg
d) 1.43 x 10^(4) kg

Respuesta :

adedayo9

Answer:

7.36 × 10^22 kg

Explanation:

Mass of the man = 90kg

Weight on the moon = 146N

radius of the moon =1.74×10^6

Weight =mg

g= weight/mass

g= 146/90 = 1.62m/s^2

From the law of gravitational force

g = GM/r^2

Where G = 6.67 ×10^-11

M = gr^2/G

M= 1.62 × (1.74×10^6)^2/6.67×10^-11

= 4.904×10^12/6.67×10^-11

=0.735×10^23

M= 7.35×10^22kg. (approximately) with option c

Lanuel

The mass of the moon is equal to: C. [tex]7.36 \times 10^{22}[/tex] kg

Given the following data:

  • Mass of man = 90 kilograms
  • Weight of man = 146 newtons.
  • Radius of moon = [tex]1.74 \times 10^6[/tex] meters

Gravitational constant = [tex]6.67 \times 10^{-11}[/tex]

To determine the mass of the moon:

First of all, we would calculate the acceleration due to gravity on the moon:

[tex]Weight = mass \times g\\\\146 = 90 \times g\\\\g=\frac{146}{90} \\\\g=1.6 \;m/s^2[/tex]

From the law of gravitational force, we have the formula:

[tex]g = \frac{Gm}{r^2}[/tex]

Where:

  • g is the acceleration due to gravity.
  • G is the gravitational constant.
  • m is the mass of a planet.
  • r is the radius.

Making m the subject of formula, we have:

[tex]m = \frac{gr^2}{G}[/tex]

Substituting the given parameters into the formula, we have;

[tex]m = \frac{1.6 \times (1.74 \times 10^6)^2}{6.67 \times 10^{-11}} \\\\m = \frac{1.6 \times 3.03 \times 10^{12}}{6.67 \times 10^{-11}}\\\\m = \frac{4.84 \times 10^{12}}{6.67 \times 10^{-11}}\\\\m = 7.36 \times 10^{22} \;kg[/tex]

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