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  • 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 state

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?
 

Option: 1

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


Option: 2

the speed is independent of radius
 


Option: 3

the period is independent of radius
 


Option: 4

the period is directly proportional to radius.


Answers (1)

best_answer

\mathrm{F= \frac{k}{r}=\frac{m v^2}{r} }

\mathrm{\Rightarrow v= \sqrt{\frac{k}{m}}=\text { constant, } v \text { is independent of radius. } }

\mathrm{ \quad T=\frac{2 \pi r}{v} \Rightarrow T \propto r}

\mathrm{T} is directly proportional to the radius.

Hence option 4 is correct.

Posted by

jitender.kumar

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