JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
Consider two physical quantities A and B related to each other as \(E=\frac{B-x^2}{A t}\) where \(E, x\) and \(t\) have dimensions of energy, length and time respectively. The dimension of \(A B\) is _______.
- A \(\mathrm{L}^{-2} \mathrm{M}^1 \mathrm{~T}^0\)
- B \(\mathrm{L}^2 \mathrm{M}^{-1} \mathrm{~T}^1\)
- C \(\mathrm{L}^{-2} \mathrm{M}^{-1} \mathrm{~T}^1\)
- D \(\mathrm{L}^0 \mathrm{M}^{-1} \mathrm{~T}^1\)
Answer & Solution
Correct Answer
(B) \(\mathrm{L}^2 \mathrm{M}^{-1} \mathrm{~T}^1\)
Step-by-step Solution
Detailed explanation
\({[B]=L^2}\) \(A=\frac{x^2}{t E}=\frac{L^2}{T^2 T^{-2}}=\frac{1}{M^{-1}}\) \({[A]=M^{-1} T}\) \({[A B]=\left[L^2 M^{-1} T^1\right]}\)
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