Explanation:
Given that,
Mass of the object, m = 7.11 kg
Spring constant of the spring, k = 61.6 N/m
Speed of the observer, ![v=2.79\times 10^8\ m/s](https://tex.z-dn.net/?f=v%3D2.79%5Ctimes%2010%5E8%5C%20m%2Fs)
We need to find the time period of oscillation observed by the observed. The time period of oscillation is given by :
![t_o=2\pi \sqrt{\dfrac{m}{k}} \\\\t_o=2\pi \sqrt{\dfrac{7.11}{61.6}} \\\\t_o=2.13\ s](https://tex.z-dn.net/?f=t_o%3D2%5Cpi%20%5Csqrt%7B%5Cdfrac%7Bm%7D%7Bk%7D%7D%20%5C%5C%5C%5Ct_o%3D2%5Cpi%20%5Csqrt%7B%5Cdfrac%7B7.11%7D%7B61.6%7D%7D%20%5C%5C%5C%5Ct_o%3D2.13%5C%20s)
Time period of oscillation measured by the observer is :
![t=\dfrac{t_o}{\sqrt{1-\dfrac{v^2}{c^2}} }\\\\t=\dfrac{2.13}{\sqrt{1-\dfrac{(2.79\times 10^8)^2}{(3\times 10^8)^2}} }\\\\t=5.79\ s](https://tex.z-dn.net/?f=t%3D%5Cdfrac%7Bt_o%7D%7B%5Csqrt%7B1-%5Cdfrac%7Bv%5E2%7D%7Bc%5E2%7D%7D%20%7D%5C%5C%5C%5Ct%3D%5Cdfrac%7B2.13%7D%7B%5Csqrt%7B1-%5Cdfrac%7B%282.79%5Ctimes%2010%5E8%29%5E2%7D%7B%283%5Ctimes%2010%5E8%29%5E2%7D%7D%20%7D%5C%5C%5C%5Ct%3D5.79%5C%20s)
So, the time period of oscillation measured by the observer is 5.79 seconds.
Generally, rings form from moons, asteroids, or comets that have disintegrated due to a collision or because they got too close to their planet (Roche Limit). ... Most of the debris, however, will not have enough energy to overcome the planet's gravity and will remain in orbit around the planet.
They almost entirely reside within galaxies because quasars are a subset of blackholes with a large and fast enough accretion disk to generate a beam of interstellar material perpendicular to itself. This typically only occurs in the largest black holes at the center of galaxies (supermassive blackholes) or at least stellar black holes---which still occur within galaxies because the material is necessary to form them.
Answer:
![A. 8.29\times 10^{-18}\ J](https://tex.z-dn.net/?f=A.%208.29%5Ctimes%2010%5E%7B-18%7D%5C%20J)
Explanation:
Given that:
p = magnitude of charge on a proton = ![1.6\times 10^{-19}\ C](https://tex.z-dn.net/?f=1.6%5Ctimes%2010%5E%7B-19%7D%5C%20C)
k = Boltzmann constant = ![9\times 10^{9}\ Nm^2/C^2](https://tex.z-dn.net/?f=9%5Ctimes%2010%5E%7B9%7D%5C%20Nm%5E2%2FC%5E2)
r = distance between the two carbon nuclei = 1.00 nm = ![1.00\times 10^{-9}\ m](https://tex.z-dn.net/?f=1.00%5Ctimes%2010%5E%7B-9%7D%5C%20m)
Since a carbon nucleus contains 6 protons.
So, charge on a carbon nucleus is ![q = 6p=6\times 1.6\times 10^{-19}\ C=9.6\times 10^{-19}\ C](https://tex.z-dn.net/?f=q%20%3D%206p%3D6%5Ctimes%201.6%5Ctimes%2010%5E%7B-19%7D%5C%20C%3D9.6%5Ctimes%2010%5E%7B-19%7D%5C%20C)
We know that the electric potential energy between two charges q and Q separated by a distance r is given by:
![U = \dfrac{kQq}{r}](https://tex.z-dn.net/?f=U%20%3D%20%5Cdfrac%7BkQq%7D%7Br%7D)
So, the potential energy between the two nuclei of carbon is as below:
![U= \dfrac{kqq}{r}\\\Rightarrow U = \dfrac{kq^2}{r}\\\Rightarrow U = \dfrac{9\times10^9\times (9.6\times 10^{-19})^2}{1.0\times 10^{-9}}\\\Rightarrow U =8.29\times 10^{-18}\ J](https://tex.z-dn.net/?f=U%3D%20%5Cdfrac%7Bkqq%7D%7Br%7D%5C%5C%5CRightarrow%20U%20%3D%20%5Cdfrac%7Bkq%5E2%7D%7Br%7D%5C%5C%5CRightarrow%20U%20%3D%20%5Cdfrac%7B9%5Ctimes10%5E9%5Ctimes%20%289.6%5Ctimes%2010%5E%7B-19%7D%29%5E2%7D%7B1.0%5Ctimes%2010%5E%7B-9%7D%7D%5C%5C%5CRightarrow%20U%20%3D8.29%5Ctimes%2010%5E%7B-18%7D%5C%20J)
Hence, the energy stored between two nuclei of carbon is
.