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JEE Main 20178 AprilOnline
Exam
JEE Main
Year
2017
Date
8 April
Mode
Online
Subject
Physics
Chapter
Units and Dimensions

JEE Main 2017 · 8 April · Online · Physics · Units and Dimensions

Time (T) , velocity (C) and angular momentum (h) are chosen as...

Time (T)\left(T\right), velocity \left(C\right)andangularmomentum(h)and angular momentum \left(h\right) are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be:

Options

  1. A[M]=[T−1C−2h]\left[M\right] = \left[{T}^{- 1}{C}^{- 2}h\right]
  2. B[M]=[T−1C2h][ M ] = [ {T}^{- 1}{C}^{2}h ]
  3. C[M]=[T−1C−2h−1]\left[M\right] = \left[{T}^{- 1}{C}^{- 2}{h}^{- 1}\right]
  4. D[M]=[TC−2h][ M ] = [ {TC}^{- 2}h ]

Correct answer

A. [M]=[T−1C−2h]\left[M\right] = \left[{T}^{- 1}{C}^{- 2}h\right]

Step-by-step solution

M ∝ {T}^{x}{C}^{y}{h}^{z}<br/><br />{M}^{1}{L}^{0}{T}^{0} = {\left({T}^{1}\right)}^{x}{\left({L}^{1}{T}^{- 1}\right)}^{y}{\left({M}^{1}{L}^{2}{T}^{- 1}\right)}^{z}<br/><br />[ {M}^{1}{L}^{0}{T}^{0} ] =[ {M}^{z}{L}^{y + 2z}{T}^{x - y - z} ]]<br/>]<br />⟹ z = 1<br/><br />y + 2z = 0, x - y - z = 0<br/><br />solving<br/><br />y = - 2<br/>and<br />andx = - 1<br/><br />M ⇒ \left[{T}^{- 1}{C}^{- 2}{h}^{1}\right]
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