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JEE Main 201910 AprilEvening Shift

Exam: JEE Main
Year: 2019
Date: 10 April
Shift: Evening Shift
Subject: Physics
Chapter: Units and Dimensions

JEE Main 2019 · 10 April · Evening Shift · Physics · Units and Dimensions

In the formula X = 5Y Z ^ 2 , X and Z have dimensions of...

In the formula

X = 5Y{Z}^{2}

,

X

and

Z

have dimensions of capacitance and magnetic field, respectively. What are the dimensions of

Y

in SI units?

Options

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

Correct answer

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

Step-by-step solution

\left[Y\right] = \dfrac{\left[X\right]}{\left[{Z}^{2}\right]}

<br/>

= \dfrac{\left[{M}^{- 1}{L}^{- 2}{T}^{4}{A}^{2}\right]}{{\left[M{L}^{0}{T}^{- 2}{A}^{- 1}\right]}^{2}}

<br/>

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

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