Two particles are moving in uniform circular motion in circles of radii R_ 1 and R_ 2 . If they experience the exact same magnitude of centripetal acceleration, the ratio of their time periods of revolution ( T_ 1 :T_ 2

Question

Quantrex Academy · Accepted Answer

Correct answer: D. R_ 1 : R_ 2

The centripetal acceleration of a particle in uniform circular motion is given by

a_{c} = \omega^{2}r

.

Since

\omega = \dfrac{2\pi}{T}

, we can write

a_{c} = \dfrac{4\pi^{2}}{T^{2}}r

.

Given that the centripetal accelerations are equal (

a_{c1} = a_{c2}

):

\dfrac{4\pi^{2}}{T_{1}^{2}}R_{1} = \dfrac{4\pi^{2}}{T_{2}^{2}}R_{2}

\Rightarrow \dfrac{T_{1}^{2}}{T_{2}^{2}} = \dfrac{R_{1}}{R_{2}}

\Rightarrow \dfrac{T_{1}}{T_{2}} = \sqrt{\dfrac{R_{1}}{R_{2}}}

Thus, the ratio of their time periods is

\sqrt{R_{1}}:\sqrt{R_{2}}

.

Answer:

\sqrt{R_{1}}:\sqrt{R_{2}}

Two particles are moving in uniform circular motion in circles of...

Options

Correct answer

Step-by-step solution

More from Motion in Two Dimensions