In the equation $S = a + bt + ct^2$,where $S$ is measured in metres and $t$ is measured in seconds,the unit of $c$ is:

If time $(t)$,velocity $(u)$,and angular momentum $(I)$ are taken as the fundamental units,then the dimension of mass $(m)$ in terms of $(t)$,$(u)$,and $(I)$ is:

$A$ 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.

The velocity of water waves $v$ may depend upon their wavelength $\lambda$,the density of water $\rho$,and the acceleration due to gravity $g$. The method of dimensions gives the relation between these quantities as:

With the usual notations,the following equation $S_t = u + \frac{1}{2}a(2t - 1)$ is

Check that the ratio $ke^{2} / G m_{e} m_{p}$ is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?