Understanding Weight and Gravity on Earth and Moon

Weight is the force exerted on an object due to gravity. It depends on two factors: the mass of the object and the acceleration due to gravity at the location. The formula for weight is:

\( W = m \times g \)

where:

• \( W \) is the weight of the object
• \( m \) is the mass of the object
• \( g \) is the acceleration due to gravity at the specific location

Unlike weight, the mass of an object is an intrinsic property and remains the same regardless of its location in the universe. A boy's mass is the same whether he is on Earth, the Moon, or in space.

The acceleration due to gravity is different on different celestial bodies. Specifically, the acceleration due to gravity on the Moon (\( g_{moon} \)) is significantly less than the acceleration due to gravity on Earth (\( g_{earth} \)). It is approximately one-sixth of Earth's gravity:

\( g_{moon} \approx \frac{1}{6} g_{earth} \)

Calculating the Boy's Mass from His Weight on the Moon

We are given the boy's weight on the Moon, \( W_{moon} = 300 \) N. Using the weight formula, we can write:

\( W_{moon} = m \times g_{moon} \)

Since \( g_{moon} \approx \frac{1}{6} g_{earth} \), we can substitute this into the equation:

\( W_{moon} = m \times \left(\frac{1}{6} g_{earth}\right) \)

We can rearrange this formula to find the mass \( m \):

\( m = \frac{W_{moon}}{\frac{1}{6} g_{earth}} = \frac{6 \times W_{moon}}{g_{earth}} \)

Determining the Boy's Weight on Earth

Now that we have an expression for the boy's mass \( m \), we can calculate his weight on Earth (\( W_{earth} \)). The formula for weight on Earth is:

\( W_{earth} = m \times g_{earth} \)

Substitute the expression for mass \( m \) we found from the Moon data:

\( W_{earth} = \left(\frac{6 \times W_{moon}}{g_{earth}}\right) \times g_{earth} \)

Notice that \( g_{earth} \) cancels out:

\( W_{earth} = 6 \times W_{moon} \)

This shows that the weight on Earth is approximately 6 times the weight on the Moon because Earth's gravity is approximately 6 times stronger than the Moon's gravity.

Now, we can plug in the given weight on the Moon, \( W_{moon} = 300 \) N:

\( W_{earth} = 6 \times 300 \text{ N} \)

\( W_{earth} = 1800 \text{ N} \)

Therefore, the weight of the same boy on the surface of the Earth will be 1800 N.

Comparison with Options

Let's compare our calculated weight with the given options:

• Option 1: 50 N
• Option 2: 300 N
• Option 3: 5 N
• Option 4: 1800 N

Our calculated value of 1800 N matches Option 4.

Revision Table: Key Physics Concepts

Additional Information on Gravity and Weight

The difference in gravity between the Earth and the Moon is due to their different masses and radii. Earth is much more massive and has a larger radius than the Moon. Gravity is directly proportional to the mass of the body and inversely proportional to the square of the distance from its center (Newton's Law of Universal Gravitation).

While we used the approximation \( g_{moon} \approx \frac{1}{6} g_{earth} \) for this calculation, the exact values are approximately \( g_{earth} \approx 9.8 \text{ m/s}^2 \) and \( g_{moon} \approx 1.62 \text{ m/s}^2 \). The ratio \( 9.8 / 1.62 \) is roughly 6.05, so the 1/6th approximation is quite accurate for many problems.

Understanding the distinction between mass and weight is crucial in physics. Mass is a measure of inertia and the amount of matter, while weight is a force. Your bathroom scale measures your weight (the force you exert on it due to gravity), but it's calibrated to show your mass on Earth by dividing your weight by the local value of \( g \).