The velocity of a wave is given by $v = \sqrt{\frac{T}{\mu}} + ax^2$, where $T$ is tension, $\mu$ is linear density, and $x$ is displacement. What are the dimensions of $a$?

The time taken by an electron to go from ground state to excited state is one shake (one shake = ${10^{ - 8}}$ s) this time in nanosecond will be

There are atomic clocks capable of measuring time with an accuracy of 1 part in ${10^{11}}$. If two such clocks are operated with precision, then after running for 5000 years, these will record