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JEE Main 20202 SeptemberMorning Shift
Exam
JEE Main
Year
2020
Date
2 September
Shift
Morning Shift
Subject
Physics
Chapter
Units and Dimensions

JEE Main 2020 · 2 September · Morning Shift · Physics · Units and Dimensions

If speed V , area A and force F are chosen as fundamental units,...

If speed VV, area AA and force FF are chosen as fundamental units, then the dimension of Young's modulus will be :

Options

  1. AFA2V−1{FA}^{2}{V}^{- 1}
  2. BFA2V−3{FA}^{2}{V}^{- 3}
  3. CFA2V−2{FA}^{2}{V}^{- 2}
  4. DFA−1V0{FA}^{- 1}{V}^{0}

Correct answer

D. FA−1V0{FA}^{- 1}{V}^{0}

Step-by-step solution

Y∝FaVbAcY=(FA)Y ∝ {F}^{a}{V}^{b}{A}^{c}Y = \left(\dfrac{F}{A}\right)

MLT−2L2∝(M1L1T−2)a(L1T−1)b(L2)c\dfrac{ML{T}^{- 2}}{{L}^{2}} ∝ {\left({M}^{1}{L}^{1}{T}^{- 2}\right)}^{a}{\left({L}^{1}{T}^{- 1}\right)}^{b}{\left({L}^{2}\right)}^{c}

M1L−1T−2∝MaLa+b+2cT−2a−b{M}^{1}{L}^{- 1}{T}^{- 2} ∝ {M}^{a}{La}^{+}b + 2cT - 2a - b

a+b+2c=–1a + b + 2c = – 1

–2a+b=–2– 2a + b = – 2

a=1,b=0,c=–1a = 1, b = 0, c = – 1

Y=F1V0A−1Y = {F}^{1}{V}^{0}{A}^{- 1}

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