JEE Advance - Physics (1988 - No. 1)
In the formula X = 3YZ2, X and Z have dimensions of capacitance and magnetic induction respectively. The dimensions of Y in MKSQ system are _____________
[M^{-3}L^{-2}T^4Q^4]
[M^{-2}L^{-2}T^4Q^4]
[M^{-3}L^{-2}T^2Q^4]
[M^{-3}L^{-2}T^4Q^2]
[M^{-3}L^{-2}T^{-4}Q^{-4}]
Explanation
$$\begin{array}{l}\begin{array}{l}\left[X\right]\;=\;\left[C\right]\;=\;\left[M^{-1}L^{-2}T^2Q^2\right]\\\left[Z\right]\;=\;\left[B\right]\;=\;\left[MT^{-1}Q^{-1}\right]\\\\\Rightarrow\;\left[Y\right]\;=\;\frac{\;\left[M^{-1}L^{-2}T^2Q^2\right]}{\;\left[MT^{-1}Q^{-1}\right]^2}\;\end{array}\\\\=\;\left[M^{-3}L^{-2}T^4Q^4\right]\\\\\\\\\\\end{array}$$
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