JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
If time \((t)\), velocity \((u)\), and angular momentum \((I)\) are taken as the fundamental units. Then the dimension of mass \(({m})\) in terms of \({t}, {u}\) and \({I}\) is
- A \([t^{-1} u^{-2}\,I^{1}]\)
- B \([t^{1} u^{2}\,I^{-1}]\)
- C \([t^{-2} u^{-1}\,I^{1}]\)
- D \([t^{-1} u^{1}\,I^{-2}]\)
Answer & Solution
Correct Answer
(A) \([t^{-1} u^{-2}\,I^{1}]\)
Step-by-step Solution
Detailed explanation
\(m \propto t^{a} v^{b} \ell^{c}\) \(m \propto[T]^{a}\left[L T^{-1}\right]^{b}\left[M L^{2} T^{-1}\right]^{c}\) \(M^{1} L^{0} T^{0}=M^{c} L^{b+2 c} T^{a-b-c}\) comparing powers \(v=1, b=-2, a=-1\) \(m \propto t^{-1} v^{-2} \ell^{1}\)
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