If the acceleration due to gravity of the earth is 6 times the acceleration due to gravity on moon, which of t

Question

If the acceleration due to gravity of the earth is 6 times the acceleration due to gravity on moon, which of the following statements is correct?

Examoogle · Accepted Answer

The correct answer is Option C: The weight of a given object is 6 times higher on the earth as compared to its weight on the moon.. Weight is defined as the force with which a body is pulled towards the center of the earth (or any celestial body), given by the product of mass and acceleration due to gravity ($W = m 	imes g$). Since mass ($m$) remains constant everywhere, the weight of an object is directly proportional to the acceleration due to gravity ($g$). Because the acceleration due to gravity on Earth is 6 times that on the Moon ($g_{	ext{earth}} = 6 	imes g_{	ext{moon}}$), the weight of an object on Earth is 6 times higher than its weight on the Moon.

Step-by-Step Solution & Concepts:
Weight is defined as the force with which a body is pulled towards the center of the earth (or any celestial body), given by the product of mass and acceleration due to gravity ($W = m 	imes g$). Since mass ($m$) remains constant everywhere, the weight of an object is directly proportional to the acceleration due to gravity ($g$). Because the acceleration due to gravity on Earth is 6 times that on the Moon ($g_{	ext{earth}} = 6 	imes g_{	ext{moon}}$), the weight of an object on Earth is 6 times higher than its weight on the Moon.

Working Principle: The gravitational force experienced by a body of mass $m$ at a location where acceleration due to gravity is $g$ is $W = mg$. Mass is an intrinsic property of matter and does not change with location, whereas acceleration due to gravity varies depending on the mass and radius of the planet or celestial body. Therefore, the ratio of weight on Earth to weight on the Moon is equal to the ratio of their respective gravitational accelerations: $\frac{W_{	ext{earth}}}{W_{	ext{moon}}} = \frac{m 	imes g_{	ext{earth}}}{m 	imes g_{	ext{moon}}} = \frac{g_{	ext{earth}}}{g_{	ext{moon}}} = 6$.

Key Formulas: $W = m 	imes g$ — Weight formula; $W_{	ext{earth}} = 6 	imes W_{	ext{moon}}$ — Relation between weights on Earth and Moon

Key Points: Mass ($m$) of an object remains constant everywhere in the universe.; Weight ($W$) is a force and varies depending on the acceleration due to gravity ($g$) at that location.; Acceleration due to gravity on the Moon is approximately one-sixth ($\frac{1}{6}$) of that on Earth.; Therefore, an object's weight on Earth is 6 times higher than its weight on the Moon.

Applications: Astronaut training and space mission weight calculations; Designing weighing instruments for different gravitational fields

Additional Info: Average acceleration due to gravity on Earth ($g_{	ext{earth}}$) $\approx 9.8 	ext{ m/s}^2$. Average acceleration due to gravity on Moon ($g_{	ext{moon}}$) $\approx 1.63 	ext{ m/s}^2$

Answer: Option C is correct — The weight of a given object is 6 times higher on the earth as compared to its weight on the moon.

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