In the formula \(X=3 Y Z^{2}, X\) and \(Z\) have the dimensions of capacitance and magnetic induction,…

In the formula \(X=3 Y Z^{2}, X\) and \(Z\) have the dimensions of capacitance and magnetic induction, respectively. The dimensions of \(Y\) in M.K.S. system are
  1. \(M^{-3} L^{-2} T^{-2} A^{-4}\)
  2. \(M L^{-2} \vec{A}\)
  3. \(M^{-3} L^{-2} T^{8} A^{4}\)
  4. \(M^{-3} L^{-2} T^{4} A^{4}\)

Solution

Here, \(X=\frac{Q}{V} .\) But \(V=\frac{W}{Q}\)
\(\therefore X=\frac{Q^{2}}{W} \cdot\) Now, \(Z=B=\frac{F}{I L}\)
\(\therefore \quad Y=\frac{X}{3 Z^{2}}=\frac{1}{3} \frac{Q^{2}}{W} \times \frac{I^{2} L^{2}}{F^{2}}\)
\(=\frac{A^{2} T^{2} A^{2} L^{2}}{\left[M L^{2} T^{-2}\right]\left[M^{2} L^{2} T^{-4}\right]}=\left[M^{-3} L^{-2} T^{8} A^{4}\right]\) ^

Asked in: JEE Mains - Units and Dimensions - Chapter Test

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