Question

The potential energy of a particle is given by the expression $U ( x )=-\alpha x +\beta \sin \frac{ x }{\gamma} .$ A dimensionless combination of the constants $\alpha, \beta$ and $\gamma$ is :-

• A. $\frac{\alpha}{\beta \gamma}$
• B. $\frac{\alpha^{2}}{\beta \alpha}$
• C. $\frac{\gamma}{\alpha \beta}$
• D. $\frac{\alpha \gamma}{\beta}$

Answer 1

Answer: (D)

$\left[\frac{ x }{\gamma}\right]$ is dimensionless
but $\left[\alpha_{x}\right]=[\beta]$ so $[x]=\left[\frac{\beta}{\alpha}\right]$
Therefore $\left[\frac{\beta}{\alpha \gamma}\right]$ or $\left[\frac{\alpha \gamma}{\beta}\right]$ is dimensionless combined