A man's mass is 72 kg on the earth. His mass on the moon will be:
72 kg
Understanding Mass on Earth vs. the Moon
The question asks about a man's mass on the moon, given his mass on the earth. To answer this, we need to understand what mass is and how it differs from weight.
What is Mass?
Mass is a fundamental property of matter. It is a measure of the amount of substance in an object. It represents the inertia of an object, which is its resistance to acceleration when a force is applied. Mass is a scalar quantity, meaning it only has magnitude, not direction.
The standard unit of mass in the International System of Units (SI) is the kilogram (kg).
What is Weight?
Weight, on the other hand, is the force exerted on an object due to gravity. It is calculated using the formula:
\( \text{Weight} = \text{Mass} \times \text{Acceleration due to gravity} \)
or \( W = mg \)
where \(W\) is weight, \(m\) is mass, and \(g\) is the acceleration due to gravity.
Weight is a vector quantity, having both magnitude and direction (towards the center of the gravitational source).
The unit of weight is typically the Newton (N).
Comparing Mass and Weight
- Mass is the amount of matter; Weight is the force of gravity.
- Mass is constant everywhere; Weight varies with gravity.
- Mass is measured in kilograms (kg); Weight is measured in Newtons (N).
Mass on Earth and the Moon
The acceleration due to gravity on the Moon is significantly less than that on Earth. Approximately, the moon's gravity is about 1/6th of Earth's gravity.
- Gravity on Earth (\(g_{\text{Earth}}\)) is approximately \(9.8 \text{ m/s}^2\).
- Gravity on the Moon (\(g_{\text{Moon}}\)) is approximately \(1.62 \text{ m/s}^2\).
Because weight depends on gravity (\(W = mg\)), an object's weight on the Moon will be about 1/6th of its weight on Earth.
However, mass does not change with location or gravity. The amount of matter in the man's body remains the same whether he is on Earth, the Moon, or in space.
Applying to the Question
Given:
- Man's mass on Earth = 72 kg
Since mass is an intrinsic property of the object (the man) and does not depend on the gravitational field, his mass will be the same everywhere.
Therefore, his mass on the Moon will be equal to his mass on Earth.
Mass on Moon = Mass on Earth = 72 kg.
The options provided relate to mass. The options are:
- 36 kg
- 12 kg
- 16 kg
- 72 kg
Based on our understanding that mass remains constant, the man's mass on the Moon will be 72 kg.
Important Questions from Gravity
Which of the following statement is correct?
I. Gravitation is a weak force unless large masses are involved.
II. The weight is equal to the product of mass and acceleration due to gravity.
The mass of the Earth is ________.
What is the reason that the value of g (acceleration due to gravity) becomes greater at the poles than at the equator?
If the acceleration due to gravity on the surface of earth is g, then the acceleration due to gravity on the surface of a planet whose mass is same as that of earth and radius is twice as that of earth is ___________.
The weight of 6 kg mass of a body on the surface of moon is about (for earth, \(g = 10 m/s^2 \) )
