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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

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?

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

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

T is directly proportional to the radius.

Hence (B) and (D) are correct.

Posted by

Ajit Kumar Dubey

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