The velocity of a freely falling body changes as ${g^p}{h^q}$ where $g$ is the acceleration due to gravity and $h$ is the height. The values of $p$ and $q$ are:

The velocity $v$ of a particle at time $t$ is given by $v = at + \frac{b}{t + c}$,where $a, b,$ and $c$ are constants. What are the dimensions of $a, b,$ and $c$ respectively?

The dimension of stopping potential $V_{0}$ in the photoelectric effect in terms of Planck's constant $h$,speed of light $c$,gravitational constant $G$,and ampere $A$ is:

The work done by a gas molecule in an isolated system is given by $W = \alpha \beta^{2} e^{-\frac{x^{2}}{\alpha kT}}$,where $x$ is the displacement,$k$ is the Boltzmann constant,$T$ is the temperature,and $\alpha$ and $\beta$ are constants. Then the dimension of $\beta$ will be:

If the force is given by $F = at + bt^2$ where $t$ is time,the dimensions of $a$ and $b$ are:

$A$ wave pulse can travel along a tense string like a violin string. $A$ series of experiments showed that the wave velocity $V$ of a pulse depends on the following quantities: the tension $T$ of the string,the cross-sectional area $A$ of the string,and the density $\rho$ (mass per unit volume) of the string. Obtain an expression for $V$ in terms of $T$,$A$,and $\rho$ using dimensional analysis.