A body of mass 60 kg weights 222 N on Mars. What is the acceleration due to gravity (in m/s 2) on Mars?
3.7
Calculating Acceleration Due to Gravity on Mars
Let's determine the acceleration due to gravity on Mars using the given information about the body's mass and weight.
Given Information
- Mass of the body (\(m\)): 60 kg
- Weight of the body on Mars (\(W_{Mars}\)): 222 N
Quantity to Find
- Acceleration due to gravity on Mars (\(g_{Mars}\))
Understanding Weight and Gravity
Weight is the force exerted on a body due to gravity. It is related to mass and the local acceleration due to gravity by the formula:
\(W = m \times g\)
Where:
- \(W\) is weight (measured in Newtons, N)
- \(m\) is mass (measured in kilograms, kg)
- \(g\) is the acceleration due to gravity (measured in meters per second squared, m/s\(^2\))
Step-by-Step Calculation of Mars Gravity
We can rearrange the formula \(W = m \times g\) to solve for \(g\):
\(g = \frac{W}{m}\)
Now, we substitute the given values for the body's weight on Mars and its mass:
\(g_{Mars} = \frac{W_{Mars}}{m}\)
\(g_{Mars} = \frac{222\, N}{60\, kg}\)
Performing the division:
\(g_{Mars} = \frac{222}{60}\, m/s^2\)
\(g_{Mars} = 3.7\, m/s^2\)
Result
The acceleration due to gravity on the surface of Mars is found to be approximately 3.7 m/s\(^2\).
This calculation shows that the gravitational pull on Mars is significantly less than on Earth (where \(g \approx 9.8\, m/s^2\)).
Revision Table: Weight, Mass, and Gravity
| Concept | Definition | Unit | Relation to Gravity |
|---|---|---|---|
| Mass (\(m\)) | The amount of matter in a body. | Kilogram (kg) | An intrinsic property of the body, independent of gravity. |
| Weight (\(W\)) | The force of gravity acting on a body. | Newton (N) | \(W = m \times g\), depends on the local acceleration due to gravity. |
| Acceleration due to Gravity (\(g\)) | The acceleration experienced by an object due to gravitational force. | m/s\(^2\) | Varies depending on the celestial body (planet, moon, etc.). |
Additional Information on Planetary Gravity
The acceleration due to gravity on a planet's surface depends primarily on its mass and radius. Larger, more massive planets generally have stronger gravitational fields, while planets with smaller radii (for a given mass) will also have stronger surface gravity.
- Earth's average gravity is about 9.8 m/s\(^2\).
- The gravity on the Moon is about 1.62 m/s\(^2\).
- Jupiter, being much more massive than Earth, has a gravitational acceleration of about 24.79 m/s\(^2\).
Understanding the concept of gravity is crucial in physics and astronomy, helping us explain planetary motion, falling objects, and much more.
Similar Questions
Fill in the blank with the most appropriate option.
The Universal Constant of Gravitation is ________.
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A. The ratio of the force of gravitation between two masses, m1 and m2, kept at a distance R on the earth and on the moon is 1:1.
B. Nm2/kg2 is the SI unit of G.
C. The value of G depends on the distance between the bodies.
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Which of the following statement is correct?
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A man's mass is 72 kg on the earth. His mass on the moon will be:
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