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An asteroid is moving directly towards the centre of the earth. When at a distance of 10 R (R is the radius of the earth) from the earth's centre, it has a speed of 12 km/s. Neglecting the effect of earth's atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is 11.2 km/s)? Give your answer to the nearest integer in kilometres/s.
Correct answer is '16'. Can you explain this answer?
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An asteroid is moving directly towards the centre of the earth. When a...
Given information:
- Distance of the asteroid from the center of the Earth when its speed is 12 km/s = 10R (R is the radius of the Earth)
- Escape velocity from the Earth's surface = 11.2 km/s
Approach:
To find the speed of the asteroid when it hits the surface of the Earth, we can use the principle of conservation of mechanical energy. At a distance of 10R from the center of the Earth, the potential energy of the asteroid is equal to the kinetic energy it possesses. We can equate these two energies to find the speed.
Calculations:
Let's assume the mass of the asteroid is 'm' and the mass of the Earth is 'M'. The potential energy (PE) and kinetic energy (KE) of the asteroid can be given as follows:
PE = -G(Mm) / r
KE = (1/2)mv^2
Where:
G is the gravitational constant
r is the distance of the asteroid from the center of the Earth
v is the speed of the asteroid
At a distance of 10R from the center of the Earth, the potential energy is equal to the kinetic energy:
-G(Mm) / (10R) = (1/2)mv^2
Simplifying the equation, we get:
v^2 = (2GM) / (10R)
To find the speed of the asteroid when it hits the surface of the Earth, we need to find the value of v when r = R (distance from the center of the Earth to the surface).
v^2 = (2GM) / R
Taking the square root of both sides, we get:
v = √[(2GM) / R]
Substituting the values of G, M, and R, we get:
v = √[(2 * 6.67430 * 10^-11 * 5.972 * 10^24) / (6.371 * 10^6)]
v ≈ 16 km/s
Therefore, the speed of the asteroid when it hits the surface of the Earth is approximately 16 km/s.
- Distance of the asteroid from the center of the Earth when its speed is 12 km/s = 10R (R is the radius of the Earth)
- Escape velocity from the Earth's surface = 11.2 km/s
Approach:
To find the speed of the asteroid when it hits the surface of the Earth, we can use the principle of conservation of mechanical energy. At a distance of 10R from the center of the Earth, the potential energy of the asteroid is equal to the kinetic energy it possesses. We can equate these two energies to find the speed.
Calculations:
Let's assume the mass of the asteroid is 'm' and the mass of the Earth is 'M'. The potential energy (PE) and kinetic energy (KE) of the asteroid can be given as follows:
PE = -G(Mm) / r
KE = (1/2)mv^2
Where:
G is the gravitational constant
r is the distance of the asteroid from the center of the Earth
v is the speed of the asteroid
At a distance of 10R from the center of the Earth, the potential energy is equal to the kinetic energy:
-G(Mm) / (10R) = (1/2)mv^2
Simplifying the equation, we get:
v^2 = (2GM) / (10R)
To find the speed of the asteroid when it hits the surface of the Earth, we need to find the value of v when r = R (distance from the center of the Earth to the surface).
v^2 = (2GM) / R
Taking the square root of both sides, we get:
v = √[(2GM) / R]
Substituting the values of G, M, and R, we get:
v = √[(2 * 6.67430 * 10^-11 * 5.972 * 10^24) / (6.371 * 10^6)]
v ≈ 16 km/s
Therefore, the speed of the asteroid when it hits the surface of the Earth is approximately 16 km/s.
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Community Answer
An asteroid is moving directly towards the centre of the earth. When a...
U1 + K1 + U2 + K2
v2 = 112.896 + 144
v = 16.027
v = 16 km/s
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An asteroid is moving directly towards the centre of the earth. When at a distance of 10 R (R is the radius of the earth) from the earths centre, it has a speed of 12 km/s. Neglecting the effect of earths atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is 11.2 km/s)? Give your answer to the nearest integer in kilometres/s.Correct answer is '16'. Can you explain this answer?
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An asteroid is moving directly towards the centre of the earth. When at a distance of 10 R (R is the radius of the earth) from the earths centre, it has a speed of 12 km/s. Neglecting the effect of earths atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is 11.2 km/s)? Give your answer to the nearest integer in kilometres/s.Correct answer is '16'. 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 An asteroid is moving directly towards the centre of the earth. When at a distance of 10 R (R is the radius of the earth) from the earths centre, it has a speed of 12 km/s. Neglecting the effect of earths atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is 11.2 km/s)? Give your answer to the nearest integer in kilometres/s.Correct answer is '16'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An asteroid is moving directly towards the centre of the earth. When at a distance of 10 R (R is the radius of the earth) from the earths centre, it has a speed of 12 km/s. Neglecting the effect of earths atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is 11.2 km/s)? Give your answer to the nearest integer in kilometres/s.Correct answer is '16'. Can you explain this answer?.
An asteroid is moving directly towards the centre of the earth. When at a distance of 10 R (R is the radius of the earth) from the earths centre, it has a speed of 12 km/s. Neglecting the effect of earths atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is 11.2 km/s)? Give your answer to the nearest integer in kilometres/s.Correct answer is '16'. 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 An asteroid is moving directly towards the centre of the earth. When at a distance of 10 R (R is the radius of the earth) from the earths centre, it has a speed of 12 km/s. Neglecting the effect of earths atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is 11.2 km/s)? Give your answer to the nearest integer in kilometres/s.Correct answer is '16'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An asteroid is moving directly towards the centre of the earth. When at a distance of 10 R (R is the radius of the earth) from the earths centre, it has a speed of 12 km/s. Neglecting the effect of earths atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is 11.2 km/s)? Give your answer to the nearest integer in kilometres/s.Correct answer is '16'. Can you explain this answer?.
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