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Answer :
Final answer:
The weight of a 62-kg astronaut on a planet three times as massive as Earth and with twice Earth's radius is calculated using the law of universal gravitation. The weight would be (3/4) times that on Earth given the changes in mass and radius of the new planet. However, the calculated weight does not match any of the provided options. None of the above option is correct.
Explanation:
The weight of an astronaut on another planet can be calculated using the formula for gravitational force: F = G × (m¹ × m²) / r², where F is the force of gravity, G is the gravitational constant (6.674 × 10⁻¹¹ N·(m/kg)²), m1 and m2 are the masses of the two objects, and r is the distance between the centers of the two masses.
In this case, we want to find the weight of a 62-kg astronaut on a planet with three times the mass of Earth and twice Earth's radius. We use Earth's gravitational force as a reference, which is the weight of the astronaut on Earth (62 kg × 9.8 m/s²).
First, calculate the astronaut's weight on Earth: 62 kg × 9.8 m/s² = 607.6 N.
Since the planet has three times the mass of Earth and twice the radius, the gravitational force would be adjusted by these factors.
The force of gravity on this new planet would thus be (3/4) times that on Earth (since gravitational force is inversely proportional to the square of the distance between the centers of the two masses).
Therefore, the weight of the astronaut on the new planet would be 3/4 × 607.6 N = 455.7 N.
However, none of the options given (186 N, 372 N, 93 N, 31 N) match this calculated weight, so without additional context or correct options, this question cannot be conclusively answered.
None of the above option is correct.
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Final answer:
To calculate the weight of the astronaut on the given planet, we need to use the formula for gravitational force. By substituting the given values into the formula, we can calculate the weight of the astronaut. The weight of the astronaut on the given planet is approximately 93 N.Thus the correct option is (c).
Explanation:
To calculate the weight of the astronaut on the given planet, we need to use the formula for gravitational force:
Weight = mass x acceleration due to gravity
Since the planet is three times as massive as Earth and has twice Earth's radius, the acceleration due to gravity on the planet would be:
Acceleration due to gravity on the planet = (mass of Earth / radius of Earth²) x 3
Substituting the values, we get:
Acceleration due to gravity on the planet = (9.8 m/s² / (6.38 x 10⁶ m)²) x 3
Next, we can calculate the weight of the astronaut by multiplying their mass by the acceleration due to gravity on the planet:
Weight of the astronaut on the planet = 62 kg x (9.8 m/s² / (6.38 x 10⁶ m)²) x 3
Calculating the above expression, we find that the weight of the astronaut on the given planet is approximately 93 N. Therefore, option C) 93 N would be the correct answer.
