JEE PYQ: Units And Dimensions Question 17
Question 17 - 2019 (10 Apr Shift 2)
In 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?
(1) $[M^{-3} L^{-2} T^8 A^4]$
(2) $[M^{-1} L^{-2} T^4 A^2]$
(3) $[M^{-2} L^0 T^{-4} A^{-2}]$
(4) $[M^{-2} L^{-2} T^6 A^3]$
Show Answer
Answer: (1)
Solution
$Y = \frac{X}{Z^2}$. $X$ = Capacitance $= [M^{-1}L^{-2}T^4A^2]$. $Z = B = [MT^{-2}A^{-1}]$. $Y = \frac{[M^{-1}L^{-2}T^4A^2]}{[MT^{-2}A^{-1}]^2} = [M^{-3}L^{-2}T^8A^4]$.
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