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1.Units, Dimensions and Measurement
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The dimensions of $\frac{\alpha}{\beta}$ in the equation $F=\frac{\alpha-t^2}{\beta v^2}$, where $F$ is the force, $v$ is velocity and $t$ is time, is ..........
A
$\left[ MLT ^{-1}\right]$
B
$\left[ ML ^{-1} T ^{-2}\right]$
C
$\left[M L^3 T^{-4}\right]$
D
$\left[ ML ^2 T ^{-4}\right]$
Solution
(c)
$F=\frac{\alpha-t^2}{\beta v^2}$
Dimensionally, $\alpha=\left[ T ^2\right]$
$\left[M L T^{-2}\right]=\frac{\left[ T ^2\right]}{\beta\left[L^2 T^{-2}\right]}$
$\beta=\frac{ T ^2}{\left[ MLT ^{-2} \cdot L ^2 T ^{-2}\right]}$
$\Rightarrow \beta=\left[ M ^{-1} L ^{-3} T ^6\right]$
Dimensions of $\frac{\alpha}{\beta}=\frac{ T ^2}{ M ^{-1} L ^{-3} T ^6}=\left[ ML ^3 T ^{-4}\right]$
Standard 11
Physics
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