Units & Measurement and Dimensions · Physics · IAT (IISER)

Two fixed point particles, each of charge $+q$, are separated by a distance $2 L$. Another point charge $+q$ of mass $m$ is oscillating about its equilibrium position as indicated in the figure below. The time period of oscillation is given by $T=$ $2 \pi^{3 / 2} \alpha \sqrt{m} / q$. Given that $\epsilon_0$ is the

permittivity of free space, which of the following options is the dimensionally correct expression for $\alpha$ in SI units?

A quantity has been measured to have a value of 0.00230 in some units. How many significant figures does the measured value have?

The fundamental constants are given to be permittivity constant $\left(\epsilon_0\right)$, Planck's constant $(h)$, velocity of light $(c)$, Newton's constant $(G)$ and Boltzmann's constant $\left(k_B\right)$. Which of the following quantities constructed out of the above constant has the dimensions of an electric charge?