Answer:
[tex]a_2 = 114.28\ m/s^2[/tex]
Explanation:
Given,
centripetal acceleration, [tex]a_1 =339\ m/s^2[/tex]
Distance from the center,[tex]r_1 = 0.0268\ m[/tex]
Centripetal acceleration,[tex] a_2 = ?[/tex]
Distance, [tex]r_2 = 0.0795\ m[/tex]
[tex]a_1 = \frac{v^2}{r_1}[/tex]
[tex] v= \dfrac{2\pi r_1}{T}[/tex]
[tex]a_1 = \frac{( \dfrac{2\pi r_1}{T})^2}{r_1}[/tex]
[tex]a_1 = \dfrac{4\pi^2 r_1}{T^2}[/tex]
similarly
[tex]a_2= \dfrac{4\pi^2 r_2}{T^2}[/tex]
now,
[tex]\dfrac{a_2}{a_1}= \dfrac{r_1}{r_2}[/tex]
[tex]a_2 = a_2\times \dfrac{r_1}{r_2}[/tex]
[tex]a_2 = 339\times \dfrac{0.0268}{0.0795}[/tex]
[tex]a_2 = 114.28\ m/s^2[/tex]
Hence, the acceleration of disc at 0.0795 m is equal to [tex]a_2 = 114.28\ m/s^2[/tex]
