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Units and Measurements — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsUnits and Measurements1 Mark
MCQ
Give force $=\frac{\alpha}{\text{Density}+\beta^3}$ What are the dimensions of $\alpha,\beta$
  • A
    $[\text{ML}^2\text{T}^{-2}][\text{ML}^{\frac{-1}{3}}]$
  • B
    $[\text{M}^2\text{L}^4\text{T}^{-2}],[\text{M}^{\frac{1}{3}}\text{L}^{-1}]$
  • ✓
    $[\text{M}^2\text{L}^{-2}\text{T}^{-2}][\text{M}^{\frac{1}{3}}\text{L}^{-1}]$
  • D
    $[\text{M}^2\text{L}^{-2}\text{T}^{-2}][\text{ML}^{-2}]$
✓

Answer

Correct option: C.
$[\text{M}^2\text{L}^{-2}\text{T}^{-2}][\text{M}^{\frac{1}{3}}\text{L}^{-1}]$
Dimensions of $\beta^3=$ Dimensions of density $=[\text{ML}^{-3}]$
$\beta=[\text{M}^{\frac{1}{3}}\text{L}^{-1}]$
Also, $\alpha=\text{Force}\times\text{Density}$
$=[\text{MLT}^{-2}][\text{ML}^{-3}]$
$=[\text{M}^2\text{L}^{-2}\text{T}^{-2}]$

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