If the unit of mass is $\alpha$ kg, unit of length is $\beta$ m and unit of time is $\gamma$ s, then the new unit of pressure is:
A$\dfrac{\alpha}{\beta\gamma^2}$ times old unit
B$\dfrac{\alpha\beta}{\gamma^2}$ times old unit
C$\dfrac{\alpha}{\beta^2\gamma^2}$ times old unit
D$\dfrac{\alpha\beta^2}{\gamma^2}$ times old unit
Answer & Solution
Correct answer: A. $\dfrac{\alpha}{\beta\gamma^2}$ times old unit
Pressure has dimensions $[ML^{-1}T^{-2}]$. Replacing the base units by $\alpha$ kg, $\beta$ m, and $\gamma$ s makes one new unit of pressure equal to $\alpha\beta^{-1}\gamma^{-2}$ times the old unit. Hence the factor is $\dfrac{\alpha}{\beta\gamma^2}$.
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