The potential energy of a point particle is given by the expression $V(x)=-\alpha x+\beta \sin (x / \gamma)$. A dimensionless combination of the constants $\alpha, \beta$ and $\gamma$ is
$\frac{\alpha}{\beta \gamma}$
$\frac{\alpha^2}{\beta \gamma}$
$\frac{\gamma}{\alpha \beta}$
$\frac{\alpha \gamma}{\beta}$
Two quantities $A$ and $B$ have different dimensions. Which mathematical operation given below is physically meaningful
The displacement of a progressive wave is represented by $y = A\,sin \,(\omega t - kx)$ where $x$ is distance and t is time. Write the dimensional formula of $(i)$ $\omega $ and $(ii)$ $k$.
$A$ and $B$ possess unequal dimensional formula then following operation is not possible in any case:-