Question

The potential energy of a point particle is given by the expression $V\left(x\right)=-\alpha x+\beta \sin \left(x/\gamma \right)$. A dimensionless combination of the constants $\alpha ,\beta$ and $\gamma$ is

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

Answer 1

Answer: (D)

$\alpha \gamma /\beta$

Dimension of $\alpha x$ should be the same as dimension of V

So $\left[\alpha \right]=ML{T}^{-2}$

dimension of $\left[\beta \right]$ will be same as of V

$\left[\beta \right]=M{L}^2{T}^{-2}$

$\left[\gamma \right]=L$

So we can see that $\frac{\alpha \gamma }{\beta }$ is dimensionless