Units & Dimensions

JEE Main level, single correct, medium

122 of 149

Question 122 of 149

In the formula X=5YZ2X=5Y{Z}^{2} , XX and ZZ have dimensions of capacitance and magnetic field, respectively. What are the dimensions of YY in SI units?

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Answer: (D) [M−3L−2T8A4]\left[{M}^{-3}{L}^{-2}{T}^{8}{A}^{4}\right]

[Y]=[X][Z2]\left[Y\right]=\dfrac{\left[X\right]}{\left[{Z}^{2}\right]}
=[M−1L−2T4A2][ML0T−2A−1]2=\dfrac{\left[{M}^{-1}{L}^{-2}{T}^{4}{A}^{2}\right]}{{\left[M{L}^{0}{T}^{-2}{A}^{-1}\right]}^{2}}
=[M−3L−2T8A4]=\left[{M}^{-3}{L}^{-2}{T}^{8}{A}^{4}\right]

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