A function $f(\theta )$ is defined as $f(\theta )\, = \,1\, - \theta + \frac{{{\theta ^2}}}{{2!}} - \frac{{{\theta ^3}}}{{3!}} + \frac{{{\theta ^4}}}{{4!}} + ...$ Why is it necessary for $f(\theta )$ to be a dimensionless quantity ?
Since, $f(\theta)$ is a sum of different power of $\theta$ and as $RHS$ is dimensionless, hence $LHS$ should also be dimensionless.
If the velocity of light $c$, universal gravitational constant $G$ and planck's constant $h$ are chosen as fundamental quantities. The dimensions of mass in the new system is
If the formula, $X=3 Y Z^{2}, X$ and $Z$ have dimensions of capacitance and magnetic induction. The dimensions of $Y$ in $M K S Q$ system are
An expression of energy density is given by $u=\frac{\alpha}{\beta} \sin \left(\frac{\alpha x}{k t}\right)$, where $\alpha, \beta$ are constants, $x$ is displacement, $k$ is Boltzmann constant and $t$ is the temperature. The dimensions of $\beta$ will be.