# consider an attractive force which is central but is inversely proportional to the first power of distance. if such a particle is in circular orbit under such a force, which of the following statements are correct

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## Consider an attractive force which is central but is inversely proportional to the first power of distance. If a particle is in circular orbit, under such a force, which of the following statements are correct?

Click here👆to get an answer to your question ✍️ Consider an attractive force which is central but is inversely proportional to the first power of distance. If a particle is in circular orbit, under such a force, which of the following statements are correct?

Question

## Consider an attractive force which is central but is inversely proportional to the first power of distance. If a particle is in circular orbit, under such a force, which of the following statements are correct?

This question has multiple correct options

**A**

## The speed is directly proportional to the square root of orbital radius

**B**

## The speed is independent of radius

**C**

## The period is independent of radius

**D**

## The period is directly proportional to radius

Medium Open in App

## A particle moves in a circular orbit under the action of a central attractive force inversely proportional to the distance 'r'. The speed of the particle is

A particle moves in a circular orbit under the action of a central attractive force inversely proportional to the distance 'r'. The speed of the particle is

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A particle moves in a circular orbit under the action of a central attractive force inversely proportional to the distance 'r'. The speed of the particle is

Question

A Proportional to r 2 B Independent of r C Proportional to r D Proportional to 1 r Open in App Solution

The correct option is **D** Independent of r

m v 2 r ∝ K r ⇒ v ∝ r ∘

i.e. speed of the particle is independent of r.

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SIMILAR QUESTIONS

**Q.**A particle moves in a circular orbit under the action of a central attractive force inversely proportional to the distance '

r

' .The speed of the particle is

**Q.**Consider an attractive force which is central but is inversely proportional to the first power of distance. If a particle is in circular orbit, under such a force, which of the following statements are correct?

**Q.**A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the

n t h

power of R. If the period of rotation of the particle is T, then.

**Q.**A particle of mass 'm' moves in a circular orbit of radius 'r' under action of an attractive force

− k 2 r 2

which always acts towards the centre of the orbit. What is the total energy in the particle?

**Q.**If the gravitational force were proportional to

1 r

, then a particle in a circular orbit under such a force would have its original speed

v [ r

is the radius of circular orbit]

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## the speed is directly proportional to the square root of orbital radius

F=(k)/(r )=(mv^(2))/(r )impliesv=sqrt((k)/(m))= constant, v is independent of radius, T=(2pir)/(v)implies T prop r T is directly proportional to the radius

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Consider an attractive force which is central but is inversely proportional to the first power of distance. If a particle is in circular orbit, under such a force , which of the following statements are correct ?

Updated On: 27-06-2022

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Text Solution Open Answer in App A

the speed is directly proportional to the square root of orbital radius

B

the speed isindependent of radius

C

the period is independent of radius

D

the period is directly proportional to radius.

Answer

The correct Answer is B::D

Solution F= k r = m v 2 r ⇒v= k m − − − √ = F=kr=mv2r⇒v=km= constant, v v

is independent of radius,

T= 2πr v ⇒T∝r T=2πrv⇒T∝r T T

is directly proportional to the radius

Answer

Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

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Guys, does anyone know the answer?