Motion In Straight Line

Question

Two masses m₁ and m₂ are separated by a distance R. What is the gravitational potential at the centre of mass?

Solution

Let the centre of mass be at a distance r₁, from m₁ and r₂ from m₂.
Then,

straight r subscript 1 equals fraction numerator straight R space straight m subscript 2 over denominator straight m subscript 1 plus straight m subscript 2 end fraction

and

straight r subscript 2 equals fraction numerator Rm subscript 1 over denominator straight m subscript 1 plus straight m subscript 2 end fraction

Gravitational potential at the centre of mass is,

straight V equals straight V subscript 1 plus straight V subscript 2 equals negative Gm subscript 1 over straight r subscript 1 minus Gm subscript 2 over straight r subscript 2

equals negative straight G open square brackets fraction numerator straight m subscript 1 left parenthesis straight m subscript 1 plus straight m subscript 2 right parenthesis over denominator straight R space straight m subscript 2 end fraction plus fraction numerator straight m subscript 2 left parenthesis straight m subscript 1 plus straight m subscript 2 right parenthesis over denominator straight R space straight m subscript 1 end fraction close square brackets

equals negative fraction numerator straight G left parenthesis straight m subscript 1 plus straight m subscript 2 right parenthesis over denominator straight R space end fraction open parentheses straight m subscript 1 over straight m subscript 2 plus straight m subscript 2 over straight m subscript 1 close parentheses

equals negative fraction numerator straight G left parenthesis straight m subscript 1 plus straight m subscript 2 right parenthesis left parenthesis straight m subscript 1 squared plus straight m subscript 2 squared right parenthesis over denominator straight R left parenthesis straight m subscript 1 straight m subscript 2 right parenthesis end fraction

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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Motion In Straight Line

Two masses m₁ and m₂ are separated by a distance R. What is the gravitational potential at the centre of mass?

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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NCERT Sample Papers

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For Daily Free Study Material Join wiredfaculty

Motion In Straight Line

Two masses m1 and m2 are separated by a distance R. What is the gravitational potential at the centre of mass?

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

Two masses m₁ and m₂ are separated by a distance R. What is the gravitational potential at the centre of mass?

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.