A particle moves in a circular orbit of radius r under a central attractive force F = − k r , k is constant. The time period of its motion is proportional to

F = m r ω 2 = k r ⇒ ω ∝ 1 r ⇒ T ∝ r

A particle moves in a circular orbit of radius r under a central attractive force F = $- \frac{k}{r},$ k is constant. The time period of its motion is proportional to

Option 1 - r1/2

Option 2 - r

Option 3 -  r2/3

Option 4 - r3/2

3 Views|Posted 4 months ago

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Vishal Baghel | Contributor-Level 10

4 months ago

Correct Option - 2

Detailed Solution:

$F = m r ω^{2} = \frac{k}{r}$

$\begin{array}{l} \Rightarrow ω \propto \frac{1}{r} \\ \Rightarrow T \propto r \end{array}$

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