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21. The mass, radius, and gravitational field intensity of the moon are [tex]7.2 \times 10^{23} \, \text{kg}[/tex], [tex]1.7 \times 10^{6} \, \text{m}[/tex], and [tex]1.66 \, \text{N/kg}[/tex] respectively.

Find the weight of a man with an 80 kg mass on the moon.



Answer :

GinnyAnswer
Sure, let's break down the solution step-by-step for the given problem.

Given:
- Mass of the man, [tex]\( m = 80 \)[/tex] kg
- Gravitational field intensity on the moon, [tex]\( g_{\text{moon}} = 1.66 \)[/tex] N/kg

To Find:
- Weight of the man on the moon.

Step-by-Step Solution:

1. Identify the formula for weight:
The weight of an object is calculated by multiplying its mass by the gravitational field intensity. This can be written as:
[tex]\[ \text{Weight} = \text{mass} \times \text{gravitational field intensity} \][/tex]

2. Substitute the given values:
- Mass ([tex]\( m \)[/tex]) = 80 kg
- Gravitational field intensity ([tex]\( g_{\text{moon}} \)[/tex]) = 1.66 N/kg

Therefore:
[tex]\[ \text{Weight on the moon} = 80 \text{ kg} \times 1.66 \text{ N/kg} \][/tex]

3. Perform the multiplication:
[tex]\[ \text{Weight on the moon} = 80 \times 1.66 \][/tex]

Using the given information, the result of this multiplication is:
[tex]\[ \text{Weight on the moon} = 132.79999999999998 \text{ N} \][/tex]

4. Result:
The weight of a man with a mass of 80 kg on the moon is approximately 132.8 N.

Thus, the weight of the man on the moon is [tex]\( 132.8 \)[/tex] N.

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