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1.Units, Dimensions and Measurement
medium
If the formula, $X=3 Y Z^{2}, X$ and $Z$ have dimensions of capacitance and magnetic induction. The dimensions of $Y$ in $M K S Q$ system are
A
$\left[M^{-3} L^{-2} T^{4} Q^{4}\right]$
B
$\left[M L^{2} T^{8} Q^{4}\right]$
C
$\left[M^{-2} L^{-3} T^{2} Q^{4}\right]$
D
$\left[M^{-2} L^{-2} T Q^{2}\right]$
(AIIMS-2017)
Solution
According to question, $[X]=[C]=\left[M^{-1} L^{-2} T^{2} Q^{2}\right]$ and $[Z]=[B]=\left[M T^{-1} Q^{-1}\right]$
$\therefore[Y]=\frac{[X]}{\left[Z^{2}\right]}$
$[Y]=\frac{\left[M^{-1} L^{-2} T^{2} Q^{2}\right]}{\left[M^{2} T^{-2} Q^{-2}\right]}=\left[M^{-3} L^{-2} T^{4} Q^{4}\right]$
Standard 11
Physics
