Calculate the velocity of an atmospheric particle 1600 km above the earth's surface, given that the radius of the earth is 6400 km and acceleration due to gravity on the surface of the earth is 9.8 m/s².

Solution

We have,
h = 1600 km
R = 6400 km = 6.4 x 10⁶ m
Therefore,
r = R + h = 6400 +1600
= 8000 m = 8.0 x 10⁶ m

Hence, escape velocity is given by,
$straight v subscript straight e space equals space square root of 2 space straight g apostrophe straight r end root space equals space square root of 2 open parentheses gR squared over straight r squared close parentheses straight r end root space space space space space space equals space square root of fraction numerator 2 space gR squared over denominator straight r end fraction end root space equals space square root of fraction numerator 2 straight x 9.8 space straight x space left parenthesis 6.4 space straight x space 10 to the power of 6 right parenthesis squared over denominator 8 space straight x space 10 to the power of 6 end fraction end root space space space space space equals space 10.02 space straight x space 10 cubed space straight m divided by straight s$

Some More Questions From Motion in Straight Line Chapter

State which of the following are examples of one, two or three dimensional motion:

(a) A kite flying in the sky.

(b) The earth revolving around the sun.

(c) A train moving along the equator of the earth in clockwise direction.

(d) Accelerated motion of a particle in a straight line.

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Motion In Straight Line

Calculate the velocity of an atmospheric particle 1600 km above the earth's surface, given that the radius of the earth is 6400 km and acceleration due to gravity on the surface of the earth is 9.8 m/s².

Some More Questions From Motion in Straight Line Chapter

Is absolute rest or absolute motion possible?

What is the most essential thing to study the motion of a body?

Can a body be always at rest in some frame?

Can a body be in motion in the frame associated with the body itself?

When an object in motion can be considered as particle or point object?

Can you think of physical phenomena involving the moon in which moon cannot be treated as particle?

A train is crossing the bridge. Can it be taken as a particle?

Can a train be taken a particle? Give an example in support of your answer.

A particle is moving along curved line in space. Is the motion one dimensional?

State which of the following are examples of one, two or three dimensional motion:

(a) A kite flying in the sky.

(b) The earth revolving around the sun.

(c) A train moving along the equator of the earth in clockwise direction.

(d) Accelerated motion of a particle in a straight line.

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For Daily Free Study Material Join wiredfaculty

Motion In Straight Line

Calculate the velocity of an atmospheric particle 1600 km above the earth's surface, given that the radius of the earth is 6400 km and acceleration due to gravity on the surface of the earth is 9.8 m/s2.

Some More Questions From Motion in Straight Line Chapter

Is absolute rest or absolute motion possible?

What is the most essential thing to study the motion of a body?

Can a body be always at rest in some frame?

Can a body be in motion in the frame associated with the body itself?

When an object in motion can be considered as particle or point object?

Can you think of physical phenomena involving the moon in which moon cannot be treated as particle?

A train is crossing the bridge. Can it be taken as a particle?

Can a train be taken a particle? Give an example in support of your answer.

A particle is moving along curved line in space. Is the motion one dimensional?

State which of the following are examples of one, two or three dimensional motion: (a) A kite flying in the sky. (b) The earth revolving around the sun. (c) A train moving along the equator of the earth in clockwise direction. (d) Accelerated motion of a particle in a straight line.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Calculate the velocity of an atmospheric particle 1600 km above the earth's surface, given that the radius of the earth is 6400 km and acceleration due to gravity on the surface of the earth is 9.8 m/s².

State which of the following are examples of one, two or three dimensional motion:

(a) A kite flying in the sky.

(b) The earth revolving around the sun.

(c) A train moving along the equator of the earth in clockwise direction.

(d) Accelerated motion of a particle in a straight line.