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JEE Main 202126 AugustMorning Shift
Exam
JEE Main
Year
2021
Date
26 August
Shift
Morning Shift
Subject
Physics
Chapter
Units and Dimensions

JEE Main 2021 · 26 August · Morning Shift · Physics · Units and Dimensions

If E, L, M and G denote the quantities as energy, angular momentum,...

If E,L,ME, L, M and GG denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of PP in the formula P=EL2M−5G−2P = E{L}^{2}{M}^{- 5}{G}^{- 2} are:

Options

  1. A[M1L1T−2]\left[{M}^{1}{L}^{1}{T}^{- 2}\right]
  2. B[M0L1T0]\left[{M}^{0}{L}^{1}{T}^{0}\right]
  3. C[M−1L−1T2]\left[{M}^{- 1}{L}^{- 1}{T}^{2}\right]
  4. D[M0L0T0]\left[{M}^{0}{L}^{0}{T}^{0}\right]

Correct answer

D. [M0L0T0]\left[{M}^{0}{L}^{0}{T}^{0}\right]

Step-by-step solution

P=EL2M−5G−2P = E{L}^{2}{M}^{- 5}{G}^{- 2}

P=[ML2T−2][ML2T−1]2[M−5][M−1L3T−2]−2P = \left[M{L}^{2}{T}^{- 2}\right]{\left[M{L}^{2}{T}^{- 1}\right]}^{2}\left[{M}^{- 5}\right]{\left[{M}^{- 1}{L}^{3}{T}^{- 2}\right]}^{- 2}

P=[M0L0T0]P = \left[{M}^{0}{L}^{0}{T}^{0}\right]

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