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1. units,dimensions and measurement — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics1. units,dimensions and measurement1 Mark
MCQ
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
  • A
    $\frac{\alpha}{\beta \gamma}$
  • B
    $\frac{\alpha^2}{\beta \gamma}$
  • C
    $\frac{\gamma}{\alpha \beta}$
  • ✓
    $\frac{\alpha \gamma}{\beta}$
✓

Answer

Correct option: D.
$\frac{\alpha \gamma}{\beta}$
d
(d)

Potential energy of the particle is

$V(x)=-\alpha x+\beta \sin \left(\frac{x}{\gamma}\right)$

Clearly, dimensions of $\alpha, \beta$ and $\gamma$ are

$[\alpha]=\frac{[ V ]}{[ x ]}=\frac{\left[ ML ^2 T ^{-2}\right]}{[ L ]}=\left[ MLT ^{-2}\right]$

$\mid \beta]=[ V ]=\left[ ML ^2 T ^{-2}\right]$

and $[\gamma]=[ x ]=[ L ]$

$=\left[ M ^0 L ^0 T ^0\right]$

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