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NEET
Exam
NEET
Subject
Physics
Chapter
Units and Dimensions

NEET · Physics · Units and Dimensions

Names of units of some physical quantities are given in List-I and...

Names of units of some physical quantities are given in List-I and their dimensions formulae are given in List-Il. Match the correct pairs in the lists <tableclass="qx−match−listqx−match−table"border="1"cellpadding="6"cellspacing="0"><tr><td><br/></td><td>amp;\textList−I</td><td>amp;\textList−II</td></tr><tr><td><br/>A.</td><td>amp;Pa−s</td><td>amp;(i)</td><td>amp;[L2T−2K−1]</td></tr><tr><td><br/>B.</td><td>amp;NmK−1</td><td>amp;(ii)</td><td>amp;[MLT−3K−1]</td></tr><tr><td><br/>C.</td><td>amp;Jkg−1K−1</td><td>amp;(iii)</td><td>amp;[ML−1T−1]</td></tr><tr><td><br/>D.</td><td>amp;Wm−1K−1</td><td>amp;(iv)</td><td>amp;[ML2T−2K−1]</td></tr><tr><td><br/><br/></td></tr></table><br/><table class="qx-match-list qx-match-table" border="1" cellpadding="6" cellspacing="0"><tr><td><br/></td><td>amp; \textList-I</td><td>amp; \textList-II</td></tr><tr><td><br/> A.</td><td>amp; Pa-s</td><td>amp; (i)</td><td>amp; {\left[L^2 T^{-2} K^{-1}\right]}</td></tr><tr><td><br/> B.</td><td>amp; NmK^{-1}</td><td>amp; (ii)</td><td>amp; {\left[MLT^{-3} K^{-1}\right]}</td></tr><tr><td><br/> C.</td><td>amp; J kg^{-1} K^{-1}</td><td>amp; (iii)</td><td>amp; {\left[ML^{-1} T^{-1}\right]}</td></tr><tr><td><br/> D.</td><td>amp; Wm^{-1} K^{-1}</td><td>amp; (iv)</td><td>amp; {\left[ML^2 T^{-2} K^{-1}\right]}</td></tr><tr><td><br/><br/></td></tr></table><br/>ABCD\begin{array}{llll}A & B & C & D\end{array}$$

Options

  1. A(iv) (iii) (i) (ii)
  2. B(iii) (ii) (iv) (i)
  3. C(iii) (i) (iv) (ii)
  4. D(iii) (iv) (i) (ii)

Correct answer

D. (iii) (iv) (i) (ii)

Step-by-step solution

Dimensions of Pa-s is =[ML−1 T−2]⋅[T]=[ML−1 T−1]\begin{aligned} & =\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right] \cdot[\mathrm{T}] \\ & =\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right] \end{aligned} Dimensions of NmK−1\mathrm{NmK}^{-1} is =[MLT−2][L][K]−1=[ML2 T−2 K−1]\begin{aligned} & =\left[\mathrm{MLT}^{-2}\right][\mathrm{L}][\mathrm{K}]^{-1} \\ & =\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right] \end{aligned} Dimensions of Jkg−1 K−1\mathrm{Jkg}^{-1} \mathrm{~K}^{-1}=[ML2 T−2][M]−1[ K]−1=[L2 T−2 K−1]\begin{aligned} & =\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right][\mathrm{M}]^{-1}[\mathrm{~K}]^{-1} \\ & =\left[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right] \end{aligned}Dimensions of $\mathrm{Wm}^{-1} \mathrm{~K}^{-1}\begin{aligned} & =\left[\mathrm{ML}^2 \mathrm{~T}^{-3}\right][\mathrm{L}]^{-1}[\mathrm{~K}]^{-1} \\ & =\left[\mathrm{MLT}^{-3} \mathrm{~K}^{-1}\right] \end{aligned}$$$ So, the correct matching is (iii), (iv), (i), (ii), hence the answer is (d).
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