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The weight of a body on the surface of earth is 392 N . What will be the weight of this body on a planet whose mass is double of earth and radius is 4 times of earth?
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The weight of a body on the surface of earth is 392 N . What will be t...
Understanding Weight on Different Planets
The weight of a body is influenced by the gravitational force exerted by the planet it is on. To calculate the weight of a body on a different planet, we can use the formula for gravitational force:
Weight (W) = G * (m * M) / R²
Where:
- W = Weight
- G = Gravitational constant
- m = Mass of the body
- M = Mass of the planet
- R = Radius of the planet
Given Data
- Weight on Earth (W_e) = 392 N
- Mass of the planet (M_p) = 2 * Mass of Earth (M_e)
- Radius of the planet (R_p) = 4 * Radius of Earth (R_e)
Step-by-Step Calculation
1. Weight on Earth:
- We know that W_e = m * g_e, where g_e is the acceleration due to gravity on Earth.
2. Finding Mass of the Body:
- From W_e = 392 N, we can express the mass (m) as:
m = W_e / g_e.
3. Acceleration due to Gravity on the New Planet:
- The new planet's gravity (g_p) can be determined using the modified formula:
g_p = G * (M_p / R_p²).
- Substituting the values:
g_p = G * (2 * M_e) / (4 * R_e)²
- This simplifies to:
g_p = (2 * G * M_e) / (16 * R_e²) = (1/8) * g_e.
4. Calculating Weight on the New Planet:
- Now, using the mass of the body (m) found earlier and the new gravity:
W_p = m * g_p = (W_e / g_e) * (1/8 * g_e) = W_e / 8 = 392 N / 8 = 49 N.
Final Answer
- Weight on the new planet: The weight of the body on the new planet is 49 N.
The weight of a body is influenced by the gravitational force exerted by the planet it is on. To calculate the weight of a body on a different planet, we can use the formula for gravitational force:
Weight (W) = G * (m * M) / R²
Where:
- W = Weight
- G = Gravitational constant
- m = Mass of the body
- M = Mass of the planet
- R = Radius of the planet
Given Data
- Weight on Earth (W_e) = 392 N
- Mass of the planet (M_p) = 2 * Mass of Earth (M_e)
- Radius of the planet (R_p) = 4 * Radius of Earth (R_e)
Step-by-Step Calculation
1. Weight on Earth:
- We know that W_e = m * g_e, where g_e is the acceleration due to gravity on Earth.
2. Finding Mass of the Body:
- From W_e = 392 N, we can express the mass (m) as:
m = W_e / g_e.
3. Acceleration due to Gravity on the New Planet:
- The new planet's gravity (g_p) can be determined using the modified formula:
g_p = G * (M_p / R_p²).
- Substituting the values:
g_p = G * (2 * M_e) / (4 * R_e)²
- This simplifies to:
g_p = (2 * G * M_e) / (16 * R_e²) = (1/8) * g_e.
4. Calculating Weight on the New Planet:
- Now, using the mass of the body (m) found earlier and the new gravity:
W_p = m * g_p = (W_e / g_e) * (1/8 * g_e) = W_e / 8 = 392 N / 8 = 49 N.
Final Answer
- Weight on the new planet: The weight of the body on the new planet is 49 N.
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The weight of a body on the surface of earth is 392 N . What will be the weight of this body on a planet whose mass is double of earth and radius is 4 times of earth?
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The weight of a body on the surface of earth is 392 N . What will be the weight of this body on a planet whose mass is double of earth and radius is 4 times of earth? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The weight of a body on the surface of earth is 392 N . What will be the weight of this body on a planet whose mass is double of earth and radius is 4 times of earth? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The weight of a body on the surface of earth is 392 N . What will be the weight of this body on a planet whose mass is double of earth and radius is 4 times of earth?.
The weight of a body on the surface of earth is 392 N . What will be the weight of this body on a planet whose mass is double of earth and radius is 4 times of earth? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The weight of a body on the surface of earth is 392 N . What will be the weight of this body on a planet whose mass is double of earth and radius is 4 times of earth? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The weight of a body on the surface of earth is 392 N . What will be the weight of this body on a planet whose mass is double of earth and radius is 4 times of earth?.
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