The formula X = 5YZ^2, X and Z have dimensions of capacitance and… - Vidyadip

MCQ

The formula $X = 5YZ^2$, $X$ and $Z$ have dimensions of capacitance and magnetic field respectively. What are the dimensions of $Y$ in $SI$ units?

A
$[{M^{ - 2}}\,{L^0}\,{T^{ - 4}}\,{A^{ - 2}}]$
✓
$[{M^{ - 3}}\,{L^{-2}}\,{T^8}\,{A^{ 4}}]$
C
$[{M^{ - 2}}\,{L^{-2}}\,{T^6}\,{A^3}]$
D
$[{M^{ - 1}}\,{L^{-2}}\,{T^4}\,{A^2}]$

✓

Answer

Correct option: B.

$[{M^{ - 3}}\,{L^{-2}}\,{T^8}\,{A^{ 4}}]$

b
$X{\kern 1pt} = 5Y{Z^2}$

$Y{\kern 1pt} = \frac{X}{{5{Z^2}}} = \,{M^{ - 3}}{L^{ - 2}}{T^8}{A^4}$

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