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An asteroid is moving directly towards the centre of the earth. when at a distance of 10R (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–1)? Give your answer to the nearest integer in kilometer
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–1)? Give your answer to the nearest integer in kilometer
Correct answer is '16'. Can you explain this answer?
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Most Upvoted Answer
An asteroid is moving directly towards the centre of the earth. when a...
To determine 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 given by:
PE = -G * (m1 * m2) / r
Where G is the gravitational constant, m1 and m2 are the masses of the asteroid and the Earth respectively, and r is the distance between the asteroid and the center of the Earth.
At this point, the kinetic energy of the asteroid is given by:
KE = (1/2) * m * v^2
Where m is the mass of the asteroid and v is its velocity.
Since the asteroid is moving directly towards the center of the Earth, the gravitational force is doing negative work on it, converting its potential energy into kinetic energy. Therefore, the sum of the potential and kinetic energies remains constant:
PE + KE = constant
At a distance of 10R from the center of the Earth, the potential energy is given by:
PE = -G * (m1 * m2) / (10R)
At this point, the kinetic energy is:
KE = (1/2) * m * (12 km/s)^2
Since the sum of the potential and kinetic energies is constant, we can equate the two expressions:
-G * (m1 * m2) / (10R) + (1/2) * m * (12 km/s)^2 = constant
We can rearrange this equation to solve for the mass of the asteroid:
m = (2 * G * (m1 * m2) / (10R * (12 km/s)^2))
Now, 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 again. At the surface of the Earth, the potential energy is zero, and only the kinetic energy remains:
KE = (1/2) * m * v^2
We want to find the value of v that satisfies this equation when m is given by the expression above.
Since the escape velocity from the Earth is 11.2 km/s, we know that the kinetic energy at the surface of the Earth is given by:
KE = (1/2) * m * (11.2 km/s)^2
Now we can equate the two expressions for the kinetic energy and solve for v:
(1/2) * m * v^2 = (1/2) * m * (11.2 km/s)^2
v^2 = (11.2 km/s)^2
v = 11.2 km/s
Therefore, the speed of the asteroid when it hits the surface of the Earth is 11.2 km/s, which is equal to the escape velocity from the Earth.
At a distance of 10R from the center of the Earth, the potential energy of the asteroid is given by:
PE = -G * (m1 * m2) / r
Where G is the gravitational constant, m1 and m2 are the masses of the asteroid and the Earth respectively, and r is the distance between the asteroid and the center of the Earth.
At this point, the kinetic energy of the asteroid is given by:
KE = (1/2) * m * v^2
Where m is the mass of the asteroid and v is its velocity.
Since the asteroid is moving directly towards the center of the Earth, the gravitational force is doing negative work on it, converting its potential energy into kinetic energy. Therefore, the sum of the potential and kinetic energies remains constant:
PE + KE = constant
At a distance of 10R from the center of the Earth, the potential energy is given by:
PE = -G * (m1 * m2) / (10R)
At this point, the kinetic energy is:
KE = (1/2) * m * (12 km/s)^2
Since the sum of the potential and kinetic energies is constant, we can equate the two expressions:
-G * (m1 * m2) / (10R) + (1/2) * m * (12 km/s)^2 = constant
We can rearrange this equation to solve for the mass of the asteroid:
m = (2 * G * (m1 * m2) / (10R * (12 km/s)^2))
Now, 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 again. At the surface of the Earth, the potential energy is zero, and only the kinetic energy remains:
KE = (1/2) * m * v^2
We want to find the value of v that satisfies this equation when m is given by the expression above.
Since the escape velocity from the Earth is 11.2 km/s, we know that the kinetic energy at the surface of the Earth is given by:
KE = (1/2) * m * (11.2 km/s)^2
Now we can equate the two expressions for the kinetic energy and solve for v:
(1/2) * m * v^2 = (1/2) * m * (11.2 km/s)^2
v^2 = (11.2 km/s)^2
v = 11.2 km/s
Therefore, the speed of the asteroid when it hits the surface of the Earth is 11.2 km/s, which is equal to the escape velocity from the Earth.
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Community Answer
An asteroid is moving directly towards the centre of the earth. when a...
Bro,
Use work energy theorem
Remember whenever velocities at two points related problems were asked WET is used
Use work energy theorem
Remember whenever velocities at two points related problems were asked WET is used
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An asteroid is moving directly towards the centre of the earth. when at a distance of 10R (R is theradius of the earth) from the earths centre, it has a speed of 12 km/s. Neglecting the effect of earthsatmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocityfrom the earth is 11.2 km/s–1)? Give your answer to the nearest integer in kilometerCorrect 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 10R (R is theradius of the earth) from the earths centre, it has a speed of 12 km/s. Neglecting the effect of earthsatmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocityfrom the earth is 11.2 km/s–1)? Give your answer to the nearest integer in kilometerCorrect 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 10R (R is theradius of the earth) from the earths centre, it has a speed of 12 km/s. Neglecting the effect of earthsatmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocityfrom the earth is 11.2 km/s–1)? Give your answer to the nearest integer in kilometerCorrect 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 10R (R is theradius of the earth) from the earths centre, it has a speed of 12 km/s. Neglecting the effect of earthsatmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocityfrom the earth is 11.2 km/s–1)? Give your answer to the nearest integer in kilometerCorrect answer is '16'. Can you explain this answer?.
An asteroid is moving directly towards the centre of the earth. when at a distance of 10R (R is theradius of the earth) from the earths centre, it has a speed of 12 km/s. Neglecting the effect of earthsatmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocityfrom the earth is 11.2 km/s–1)? Give your answer to the nearest integer in kilometerCorrect 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 10R (R is theradius of the earth) from the earths centre, it has a speed of 12 km/s. Neglecting the effect of earthsatmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocityfrom the earth is 11.2 km/s–1)? Give your answer to the nearest integer in kilometerCorrect 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 10R (R is theradius of the earth) from the earths centre, it has a speed of 12 km/s. Neglecting the effect of earthsatmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocityfrom the earth is 11.2 km/s–1)? Give your answer to the nearest integer in kilometerCorrect 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 10R (R is theradius of the earth) from the earths centre, it has a speed of 12 km/s. Neglecting the effect of earthsatmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocityfrom the earth is 11.2 km/s–1)? Give your answer to the nearest integer in kilometerCorrect answer is '16'. Can you explain this answer?, a detailed solution for An asteroid is moving directly towards the centre of the earth. when at a distance of 10R (R is theradius of the earth) from the earths centre, it has a speed of 12 km/s. Neglecting the effect of earthsatmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocityfrom the earth is 11.2 km/s–1)? Give your answer to the nearest integer in kilometerCorrect answer is '16'. Can you explain this answer? has been provided alongside types of An asteroid is moving directly towards the centre of the earth. when at a distance of 10R (R is theradius of the earth) from the earths centre, it has a speed of 12 km/s. Neglecting the effect of earthsatmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocityfrom the earth is 11.2 km/s–1)? Give your answer to the nearest integer in kilometerCorrect answer is '16'. Can you explain this answer? theory, EduRev gives you an
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