# In the formula $\mathrm{X}=5 \mathrm{YZ}^{2}, \mathrm{X}$ and $\mathrm{Z}$ have dimensions of capacitance and magnetic field, respectively. What are the dimensions of $\mathrm{Y}$ in SI units ?

Question:

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

1. $\left[\mathrm{M}^{-3} \mathrm{~L}^{-2} \mathrm{~T}^{8} \mathrm{~A}^{4}\right]$

2. $\left[\mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{4} \mathrm{~A}^{2}\right]$

3. $\left[\mathrm{M}^{-2} \mathrm{~L}^{0} \mathrm{~T}^{-4} \mathrm{~A}^{-2}\right]$

4. $\left[\mathrm{M}^{-2} \mathrm{~L}^{-2} \mathrm{~T}^{6} \mathrm{~A}^{3}\right]$

JEE Main Previous Year Single Correct Question of JEE Main from Chemistry Laws of Motion chapter.

JEE Main Previous Year 2019

Correct Option: 1

Solution:

\begin{aligned}

&\text {} \mathrm{X}=5 \mathrm{YZ}^{2} \\

&\Rightarrow Y \propto \frac{X}{Z^{2}}

\end{aligned}

\begin{aligned}

&X=\text { Capacitance }=\frac{Q}{\mathrm{~V}}=\frac{Q^{2}}{W}=\frac{\left[A^{2} T^{2}\right]}{\left[M L^{2} T^{-2}\right]} \\

&\mathrm{X}=\left[\mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{4} \mathrm{~A}^{2}\right] \\

&Z=B=\frac{F}{I L} \\

&\mathrm{Z}=\left[\mathrm{MT}^{-2} \mathrm{~A}^{-1}\right] \\

&Y=\frac{\left[M^{-1} L^{-2} T^{4} A^{2}\right]}{\left[M T^{-2} A^{-1}\right]^{2}}

\end{aligned}

$\mathrm{Y}=\left[\mathrm{M}^{-3} \mathrm{~L}^{-2} \mathrm{~T}^{8} \mathrm{~A}^{4}\right]$

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