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Two astronauts have deserted their spaceship in a region of space far from the gravitational attraction of any other body. Each has a mass of 100 kg and they are 100 m apart. They are initially at rest relative to each other. How long (in number of days) will it be before the gravitational attraction brings them 1 cm closer together? (Nearest integer)
Correct answer is '1'. Can you explain this answer?
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Two astronauts have deserted their spaceship in a region of space far...
Given information:
- Two astronauts have deserted their spaceship in a region of space far from the gravitational attraction of any other body.
- Each astronaut has a mass of 100 kg.
- They are initially 100 m apart.
- They are at rest relative to each other.
Objective:
To determine the time it takes for the gravitational attraction to bring the astronauts 1 cm closer together.
Assumptions:
- The astronauts can be treated as point masses.
- The gravitational force between the astronauts can be approximated using Newton's law of universal gravitation.
Using Newton's law of universal gravitation:
The force between two objects with masses m1 and m2, separated by a distance r, is given by the equation:
F = G * (m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2), m1 and m2 are the masses of the objects, and r is the distance between the objects.
Applying Newton's law of universal gravitation:
- Determine the gravitational force between the astronauts at the initial distance of 100 m:
- F_initial = G * (m1 * m2) / r^2
- F_initial = (6.67430 × 10^-11) * (100 * 100) / (100^2)
- F_initial = 6.67430 × 10^-11 N
- Determine the gravitational force between the astronauts at a distance 1 cm (0.01 m) closer together:
- F_final = G * (m1 * m2) / (r - 0.01)^2
- F_final = (6.67430 × 10^-11) * (100 * 100) / (100 - 0.01)^2
- F_final = 6.67430 × 10^-11 N
Calculating the time:
- Determine the acceleration of the astronauts due to the gravitational force:
- F = m * a
- a = F / m
- a = (F_final - F_initial) / m
- a = (6.67430 × 10^-11 - 6.67430 × 10^-11) / 100
- a = 0 m/s^2
- Use the kinematic equation to determine the time it takes for the astronauts to move 1 cm closer together:
- d = v_initial * t + (1/2) * a * t^2
- 0.01 = 0 * t + (1/2) * 0 * t^2
- 0.01 = 0
- This equation has no solution, indicating that the astronauts will not move 1 cm closer together due to gravitational attraction.
Conclusion:
Since the astronauts are in space far from any other gravitational attraction, they will not move closer together due to gravitational attraction. Therefore, the answer is 0 days, not 1 day.
- Two astronauts have deserted their spaceship in a region of space far from the gravitational attraction of any other body.
- Each astronaut has a mass of 100 kg.
- They are initially 100 m apart.
- They are at rest relative to each other.
Objective:
To determine the time it takes for the gravitational attraction to bring the astronauts 1 cm closer together.
Assumptions:
- The astronauts can be treated as point masses.
- The gravitational force between the astronauts can be approximated using Newton's law of universal gravitation.
Using Newton's law of universal gravitation:
The force between two objects with masses m1 and m2, separated by a distance r, is given by the equation:
F = G * (m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2), m1 and m2 are the masses of the objects, and r is the distance between the objects.
Applying Newton's law of universal gravitation:
- Determine the gravitational force between the astronauts at the initial distance of 100 m:
- F_initial = G * (m1 * m2) / r^2
- F_initial = (6.67430 × 10^-11) * (100 * 100) / (100^2)
- F_initial = 6.67430 × 10^-11 N
- Determine the gravitational force between the astronauts at a distance 1 cm (0.01 m) closer together:
- F_final = G * (m1 * m2) / (r - 0.01)^2
- F_final = (6.67430 × 10^-11) * (100 * 100) / (100 - 0.01)^2
- F_final = 6.67430 × 10^-11 N
Calculating the time:
- Determine the acceleration of the astronauts due to the gravitational force:
- F = m * a
- a = F / m
- a = (F_final - F_initial) / m
- a = (6.67430 × 10^-11 - 6.67430 × 10^-11) / 100
- a = 0 m/s^2
- Use the kinematic equation to determine the time it takes for the astronauts to move 1 cm closer together:
- d = v_initial * t + (1/2) * a * t^2
- 0.01 = 0 * t + (1/2) * 0 * t^2
- 0.01 = 0
- This equation has no solution, indicating that the astronauts will not move 1 cm closer together due to gravitational attraction.
Conclusion:
Since the astronauts are in space far from any other gravitational attraction, they will not move closer together due to gravitational attraction. Therefore, the answer is 0 days, not 1 day.
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Community Answer
Two astronauts have deserted their spaceship in a region of space far...
a1 = acceleration of first
a2 = acceleration of second
Net acceleration for approach
Now 
Solving , we get t = 1.41 days
≈ 1 day
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Two astronauts have deserted their spaceship in a region of space far from the gravitational attraction of any other body. Each has a mass of 100 kg and they are 100 m apart. They are initially at rest relative to each other. How long (in number of days) will it be before the gravitational attraction brings them 1 cm closer together? (Nearest integer)Correct answer is '1'. Can you explain this answer?
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Two astronauts have deserted their spaceship in a region of space far from the gravitational attraction of any other body. Each has a mass of 100 kg and they are 100 m apart. They are initially at rest relative to each other. How long (in number of days) will it be before the gravitational attraction brings them 1 cm closer together? (Nearest integer)Correct answer is '1'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two astronauts have deserted their spaceship in a region of space far from the gravitational attraction of any other body. Each has a mass of 100 kg and they are 100 m apart. They are initially at rest relative to each other. How long (in number of days) will it be before the gravitational attraction brings them 1 cm closer together? (Nearest integer)Correct answer is '1'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two astronauts have deserted their spaceship in a region of space far from the gravitational attraction of any other body. Each has a mass of 100 kg and they are 100 m apart. They are initially at rest relative to each other. How long (in number of days) will it be before the gravitational attraction brings them 1 cm closer together? (Nearest integer)Correct answer is '1'. Can you explain this answer?.
Two astronauts have deserted their spaceship in a region of space far from the gravitational attraction of any other body. Each has a mass of 100 kg and they are 100 m apart. They are initially at rest relative to each other. How long (in number of days) will it be before the gravitational attraction brings them 1 cm closer together? (Nearest integer)Correct answer is '1'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two astronauts have deserted their spaceship in a region of space far from the gravitational attraction of any other body. Each has a mass of 100 kg and they are 100 m apart. They are initially at rest relative to each other. How long (in number of days) will it be before the gravitational attraction brings them 1 cm closer together? (Nearest integer)Correct answer is '1'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two astronauts have deserted their spaceship in a region of space far from the gravitational attraction of any other body. Each has a mass of 100 kg and they are 100 m apart. They are initially at rest relative to each other. How long (in number of days) will it be before the gravitational attraction brings them 1 cm closer together? (Nearest integer)Correct answer is '1'. Can you explain this answer?.
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Two astronauts have deserted their spaceship in a region of space far from the gravitational attraction of any other body. Each has a mass of 100 kg and they are 100 m apart. They are initially at rest relative to each other. How long (in number of days) will it be before the gravitational attraction brings them 1 cm closer together? (Nearest integer)Correct answer is '1'. Can you explain this answer?, a detailed solution for Two astronauts have deserted their spaceship in a region of space far from the gravitational attraction of any other body. Each has a mass of 100 kg and they are 100 m apart. They are initially at rest relative to each other. How long (in number of days) will it be before the gravitational attraction brings them 1 cm closer together? (Nearest integer)Correct answer is '1'. Can you explain this answer? has been provided alongside types of Two astronauts have deserted their spaceship in a region of space far from the gravitational attraction of any other body. Each has a mass of 100 kg and they are 100 m apart. They are initially at rest relative to each other. How long (in number of days) will it be before the gravitational attraction brings them 1 cm closer together? (Nearest integer)Correct answer is '1'. Can you explain this answer? theory, EduRev gives you an
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