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The moon's radius is 1/4 that of the earth and its mass is 1/80 times that of the earth. If g represents the acceleration due to gravity on the surface of the earth, then on the surface of the moon its value is
- a)ge/ 4
- b)ge/ 5
- c)ge/ 6
- d)ge/ 8
Correct answer is option 'B'. Can you explain this answer?
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Question Analysis:
The question states that the radius of the moon is 1/4 of the radius of the earth, and the mass of the moon is 1/80 times the mass of the earth. We need to find the value of acceleration due to gravity on the surface of the moon (g_moon) in terms of the acceleration due to gravity on the surface of the earth (g_earth).
Given Data:
Radius of the moon (R_moon) = 1/4 * Radius of the earth (R_earth)
Mass of the moon (M_moon) = 1/80 * Mass of the earth (M_earth)
Calculating the Value of g_moon:
The acceleration due to gravity on the surface of a planet or moon can be calculated using the formula:
g = G * M / R^2
Where:
g is the acceleration due to gravity,
G is the gravitational constant (approximately 6.67 x 10^-11 N m^2/kg^2),
M is the mass of the planet or moon, and
R is the radius of the planet or moon.
To find the value of g_moon, we can compare the ratio of g_moon to g_earth using the given information.
Step 1: Calculate the value of g_earth using the mass and radius of the earth.
g_earth = G * M_earth / R_earth^2
Step 2: Calculate the value of g_moon using the mass and radius of the moon.
g_moon = G * M_moon / R_moon^2
Step 3: Substitute the given values into the equations.
g_earth = G * M_earth / R_earth^2
g_moon = G * M_moon / R_moon^2
Since R_moon = 1/4 * R_earth and M_moon = 1/80 * M_earth, we can substitute these values into the equation for g_moon.
g_moon = G * (1/80 * M_earth) / ((1/4 * R_earth)^2)
g_moon = G * (1/80 * M_earth) / (1/16 * R_earth^2)
Simplifying the equation further:
g_moon = (1/80) * (16/1) * (G * M_earth / R_earth^2)
g_moon = G * M_earth / (80 * R_earth^2)
Step 4: Compare the ratio of g_moon to g_earth.
g_moon / g_earth = (G * M_earth / (80 * R_earth^2)) / (G * M_earth / R_earth^2)
g_moon / g_earth = (G * M_earth * R_earth^2) / (80 * R_earth^2 * G * M_earth)
Simplifying the equation further:
g_moon / g_earth = 1/80
Therefore, the value of g_moon is 1/80 times the value of g_earth.
Conclusion:
The value of acceleration due to gravity on the surface of the moon
The question states that the radius of the moon is 1/4 of the radius of the earth, and the mass of the moon is 1/80 times the mass of the earth. We need to find the value of acceleration due to gravity on the surface of the moon (g_moon) in terms of the acceleration due to gravity on the surface of the earth (g_earth).
Given Data:
Radius of the moon (R_moon) = 1/4 * Radius of the earth (R_earth)
Mass of the moon (M_moon) = 1/80 * Mass of the earth (M_earth)
Calculating the Value of g_moon:
The acceleration due to gravity on the surface of a planet or moon can be calculated using the formula:
g = G * M / R^2
Where:
g is the acceleration due to gravity,
G is the gravitational constant (approximately 6.67 x 10^-11 N m^2/kg^2),
M is the mass of the planet or moon, and
R is the radius of the planet or moon.
To find the value of g_moon, we can compare the ratio of g_moon to g_earth using the given information.
Step 1: Calculate the value of g_earth using the mass and radius of the earth.
g_earth = G * M_earth / R_earth^2
Step 2: Calculate the value of g_moon using the mass and radius of the moon.
g_moon = G * M_moon / R_moon^2
Step 3: Substitute the given values into the equations.
g_earth = G * M_earth / R_earth^2
g_moon = G * M_moon / R_moon^2
Since R_moon = 1/4 * R_earth and M_moon = 1/80 * M_earth, we can substitute these values into the equation for g_moon.
g_moon = G * (1/80 * M_earth) / ((1/4 * R_earth)^2)
g_moon = G * (1/80 * M_earth) / (1/16 * R_earth^2)
Simplifying the equation further:
g_moon = (1/80) * (16/1) * (G * M_earth / R_earth^2)
g_moon = G * M_earth / (80 * R_earth^2)
Step 4: Compare the ratio of g_moon to g_earth.
g_moon / g_earth = (G * M_earth / (80 * R_earth^2)) / (G * M_earth / R_earth^2)
g_moon / g_earth = (G * M_earth * R_earth^2) / (80 * R_earth^2 * G * M_earth)
Simplifying the equation further:
g_moon / g_earth = 1/80
Therefore, the value of g_moon is 1/80 times the value of g_earth.
Conclusion:
The value of acceleration due to gravity on the surface of the moon
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The moons radius is 1/4 that of the earth and its mass is 1/80 times that of the earth. If g represents the acceleration due to gravity on the surface of the earth, then on the surface of the moon its value isa)ge/ 4b)ge/ 5c)ge/ 6d)ge/ 8Correct answer is option 'B'. Can you explain this answer?
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