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NEET 2009
Exam
NEET
Year
2009
Subject
Physics
Chapter
Units and Dimensions

NEET 2009 · Physics · Units and Dimensions

If the dimensions of a physical quantity are given by M^ a L^ b T^c...

If the dimensions of a physical quantity are given by MaLbTc\mathrm{M}^{\mathrm{a}} \mathrm{L}^{\mathrm{b}} \mathrm{T}^c, then the physical quantity will be

Options

  1. Apressure if a=1, b=−1,c=−2\mathrm{a}=1, \mathrm{~b}=-1, \mathrm{c}=-2
  2. Bvelocity if a=1,b=0,c=−1a=1, b=0, c=-1
  3. Cacceleration if a =1,b=1,c=−2=1, b=1, c=-2
  4. Dforce if a=0, b=−1,c=−2\mathrm{a}=0, \mathrm{~b}=-1, \mathrm{c}=-2

Correct answer

A. pressure if a=1, b=−1,c=−2\mathrm{a}=1, \mathrm{~b}=-1, \mathrm{c}=-2

Step-by-step solution

(i) Dimensions of velocity =[M0 L1 T−1]=\left[\mathrm{M}^0 \mathrm{~L}^1 \mathrm{~T}^{-1}\right] Here, a=0,b=1,c=−1a=0, b=1, c=-1 (ii) Dimensions of acceleration =[M0 L1 T−2]=\left[\mathrm{M}^0 \mathrm{~L}^1 \mathrm{~T}^{-2}\right] Here, a=0,b=1,c=−2\quad a=0, b=1, c=-2 (iii) Dimensions of force =[M1 L1 T−2]=\left[\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^{-2}\right] Here, a=1,b=1,T=−2a=1, b=1, T=-2 (iv) Dimensions of pressure =[M1 L−1 T−2]=\left[\mathrm{M}^1 \mathrm{~L}^{-1} \mathrm{~T}^{-2}\right] ∴\therefore Here, a=1, b=−1,c=−2\quad \mathrm{a}=1, \mathrm{~b}=-1, \mathrm{c}=-2 ∴\therefore The physical quantity is pressure.
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