Question:
In the formula $X = 3Y\, Z^{2}, X$ and $Z$ have dimensions of capacitance and magnetic induction respectively. What are the dimensions of $Y$ in $MKSQ$ system?
In the formula $X = 3Y\, Z^{2}, X$ and $Z$ have dimensions of capacitance and magnetic induction respectively. What are the dimensions of $Y$ in $MKSQ$ system?
Updated On: Jun 14, 2022
- $ [ L^{ - 3} L ^{ - 1} T^3 Q^4 ]$
- $ [ M^{ - 3} L^{ - 2} T^4 Q^4 ] $
- $ [ M^{ - 2} L^{ - 2} T^4 q^4 ] $
- $ [ M^{ - 3} L^{ - 2} T^4 Q] $
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The Correct Option is B
Solution and Explanation
[ Y ] = $ \bigg [ \frac{ X}{ Z^2} \bigg ] = \bigg [ \frac{ \text{Capacitance} }{ (\text{Magnetic induction} )^2 } \bigg ] $
= $ \bigg [ \frac{ M^{ - 1} L^{ - 2} Q^2 T^2 }{ M^2 Q^ { - 2} T^{ - 2}} \bigg ] $
= $ [ M^{ - 3} L^{ - 2} T^4 Q^4 ] $
= $ \bigg [ \frac{ M^{ - 1} L^{ - 2} Q^2 T^2 }{ M^2 Q^ { - 2} T^{ - 2}} \bigg ] $
= $ [ M^{ - 3} L^{ - 2} T^4 Q^4 ] $
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