The energy of a photon is given by $E = h

u$, where$h$is Planck's constant and$

u$is the frequency. If a new quantity$X$is defined as$X = \frac{h^2

u^3}{E}$, the dimensions of$X$ are:

In the relation $p = \frac{{\rm{\alpha }}}{{\rm{\beta }}}{\rm{\;}}{{\rm{e}}^{ - \frac{{\alpha z}}{{k{\rm{heta }}}}}},{\rm{\;}}p$ , is the pressure, z the distance, k is Boltzmann constant and $heta$ is the temperature, the dimensional formula of $\beta$ will be

If $S = \frac{1}{3}f{t^3},f$ has the dimensions of

The energy (E), angular momentum (L) and universal gravitational constant (G) are chosen as fundamental quantities. The dimensions of universal gravitational constant in the dimensional formula of Planck’s constant (h) is

If the speed of light (c), Planck's constant (h), and gravitational constant (G) are chosen as fundamental units, then the dimension of time is:

If $E$ represents the rest mass energy of a particle and $G$ is the gravitational constant, which of the following represents the dimensions of $\sqrt{\frac{E}{G}}$?

If force (F), acceleration (A), and time (T) are chosen as fundamental quantities, what are the dimensions of energy?

Let the speed of light be $c$, the universal gravitational constant be $G$, and the electrostatic force constant be $k = \frac{1}{4\pi\epsilon_0}$. If $q$ represents an electric charge, determine the expression for a length $l$ that can be formed from these quantities.

The velocity of a body is given by the equation $v = \frac{b}{t} + c{t^2} + d{t^2}$ The dimensional formula of b is

If p represents radiation pressure, C represents speed of light and q represents radiation energy striking a unit area per second, then non-zero integers a,b and c are such that ${p^a}{q^b}{C^c}$ is dimensionless, then

A gas bubble from an explosion under water oscillates with a time period T, depends upon static pressure p, density of water $\rho$ and the total energy of explosion E. Find the expression for the time period T.(where, k is a dimensionless constant)