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

  • [KVPY 2012]
  • A

    $\frac{\alpha}{\beta \gamma}$

  • B

    $\frac{\alpha^2}{\beta \gamma}$

  • C

    $\frac{\gamma}{\alpha \beta}$

  • D

    $\frac{\alpha \gamma}{\beta}$

Similar Questions

If force $(F)$, velocity $(V)$ and time $(T)$ are considered as fundamental physical quantity, then dimensional formula of density will be:

  • [JEE MAIN 2023]

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:-

The equation of the stationary wave is
$y = 2A\,\,\sin \,\left( {\frac{{2\pi ct}}{\lambda }} \right)\,\cos \,\,\,\left( {\frac{{2\pi x}}{\lambda }} \right)$
Which statement is not true?