An object weighs 9 N on the surface of the Earth. What would be its weight, when measured on the surface of a planet where the acceleration due to gravity is 9 times that on the surface of the Earth?
The weight would become 9 times
Understanding Weight and Gravity
Weight is the force exerted on an object due to gravity. It depends on two factors: the object's mass and the acceleration due to gravity at its location. The formula for weight is given by:
\(W = m \times g\)
where:
- \(W\) is the weight of the object (measured in Newtons, N)
- \(m\) is the mass of the object (measured in kilograms, kg)
- \(g\) is the acceleration due to gravity at the specific location (measured in \(m/s^2\))
Mass is an intrinsic property of the object and remains constant regardless of where it is located in the universe. However, acceleration due to gravity (\(g\)) varies from one celestial body (like Earth, a planet, or the Moon) to another, and even slightly at different locations on the same body. Therefore, the weight of an object changes with the change in acceleration due to gravity.
Calculating Weight on the Planet
Let's consider the given information:
- Weight of the object on the surface of the Earth, \(W_E = 9\) N.
- Let \(g_E\) be the acceleration due to gravity on the surface of the Earth.
- Let \(m\) be the mass of the object.
Using the weight formula for Earth:
\(W_E = m \times g_E\)
\(9 \text{ N} = m \times g_E\)
Now, consider the planet. Let \(W_P\) be the weight of the object on the surface of this planet and \(g_P\) be the acceleration due to gravity on the surface of this planet. We are given that the acceleration due to gravity on the planet is 9 times that on Earth:
\(g_P = 9 \times g_E\)
The weight of the object on the planet is:
\(W_P = m \times g_P\)
Substitute the relationship between \(g_P\) and \(g_E\):
\(W_P = m \times (9 \times g_E)\)
\(W_P = 9 \times (m \times g_E)\)
From our equation for weight on Earth, we know that \(m \times g_E = W_E = 9\) N. Substitute this into the equation for \(W_P\):
\(W_P = 9 \times W_E\)
\(W_P = 9 \times 9 \text{ N}\)
\(W_P = 81 \text{ N}\)
So, the weight of the object on the surface of the planet would be 81 N. This is 9 times the weight on Earth (which was 9 N).
Analyzing the Options
Let's look at the given options based on our calculation:
- Option 1: The weight would remain the same. This is incorrect because the acceleration due to gravity changes, and weight depends on gravity.
- Option 2: The weight would be equal to 1 N. This would mean the weight is reduced to \(1/9\)th of the original weight, which is incorrect as gravity increased.
- Option 3: The weight would become 9 times. The original weight was 9 N. 9 times the original weight is \(9 \times 9 \text{ N} = 81\) N. Our calculation shows the weight on the planet is 81 N, which is indeed 9 times the weight on Earth. This option correctly describes the result.
- Option 4: The weight will be reduced to \(\frac{1}{9}\) N. This implies the weight becomes \(1/81\)th of the original weight (\(9 \text{ N} \times \frac{1}{81} = \frac{1}{9}\text{ N}\)), which is incorrect. The weight increases when gravity increases.
Our analysis confirms that when the acceleration due to gravity becomes 9 times, the weight also becomes 9 times, assuming the mass remains constant.
Conclusion on Weight Change
Since the acceleration due to gravity on the planet is 9 times that on Earth, and weight is directly proportional to gravity (\(W \propto g\) when mass \(m\) is constant), the weight of the object on the planet will be 9 times its weight on Earth.
Revision Table: Weight vs. Gravity
| Concept | Definition | Formula | How it changes with location |
|---|---|---|---|
| Mass (\(m\)) | Amount of matter in an object | Intrinsic property (no formula needed to define it directly) | Remains constant everywhere |
| Weight (\(W\)) | Force of gravity on an object | \(W = m \times g\) | Changes with the acceleration due to gravity (\(g\)) |
Additional Information: Mass vs. Weight
It's important to distinguish between mass and weight. Mass is a measure of the amount of matter in an object. It is a scalar quantity and is measured in kilograms (kg). Mass is an intrinsic property of the object and does not change with its location.
Weight, on the other hand, is the force of gravity acting on an object's mass. It is a vector quantity and is measured in Newtons (N). Weight depends on both the object's mass and the local acceleration due to gravity. If gravity changes, weight changes, but mass stays the same.
In this problem, the object's mass remains the same whether it is on Earth or on the planet. However, because the acceleration due to gravity is 9 times stronger on the planet, the gravitational force pulling on the object (its weight) is also 9 times stronger.
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Important Questions from Gravity
Which of the following law states that, "The force between two objects is directly proportional to the product of their masses?"
Which of the following statements about the movement of planets is true?
A. A planet's orbit is elliptical with the Sun at one of two focal points.
B. The orbit of a planet is circular with the sun in the center.
C. The orbit of a planet is elliptical with another planet in one of the two center-points.
D. The orbit of a planet is circular with another planet in the center.
If the mass of a person is 60 kg on the surface of earth then the same person’s mass on the surface of the moon will be:
The centripetal force required to keep the moon in its orbit is provided by which force?
How is the acceleration due to gravity denoted?
