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Question:
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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
$\begin{array}{ll|ll}
\hline & \text{ List-I } & \text{ List-II } \\
\hline A. & \mathrm{Pa}-\mathrm{s} & (i) & {\left[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]} \\
\hline B. & \mathrm{NmK}^{-1} & (ii) & {\left[\mathrm{MLT}^{-3} \mathrm{~K}^{-1}\right]} \\
\hline C. & \mathrm{J} \mathrm{kg}^{-1} \mathrm{~K}^{-1} & (iii) & {\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right]} \\
\hline D. & \mathrm{Wm}^{-1} \mathrm{~K}^{-1} & (iv) & {\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]} \\
\hline
\end{array}$
$\begin{array}{llll}A & B & C & D\end{array}$
Options:
$\begin{array}{ll|ll}
\hline & \text{ List-I } & \text{ List-II } \\
\hline A. & \mathrm{Pa}-\mathrm{s} & (i) & {\left[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]} \\
\hline B. & \mathrm{NmK}^{-1} & (ii) & {\left[\mathrm{MLT}^{-3} \mathrm{~K}^{-1}\right]} \\
\hline C. & \mathrm{J} \mathrm{kg}^{-1} \mathrm{~K}^{-1} & (iii) & {\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right]} \\
\hline D. & \mathrm{Wm}^{-1} \mathrm{~K}^{-1} & (iv) & {\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]} \\
\hline
\end{array}$
$\begin{array}{llll}A & B & C & D\end{array}$
Solution:
2492 Upvotes
Verified Answer
The correct answer is:
(iii) (iv) (i) (ii)
Dimensions of Pa-s is
$\begin{aligned}
& =\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right] \cdot[\mathrm{T}] \\
& =\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right]
\end{aligned}$
Dimensions of $\mathrm{NmK}^{-1}$ is
$\begin{aligned}
& =\left[\mathrm{MLT}^{-2}\right][\mathrm{L}][\mathrm{K}]^{-1} \\
& =\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]
\end{aligned}$
Dimensions of $\mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$
$\begin{aligned}
& =\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right][\mathrm{M}]^{-1}[\mathrm{~K}]^{-1} \\
& =\left[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]
\end{aligned}$
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).
$\begin{aligned}
& =\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right] \cdot[\mathrm{T}] \\
& =\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right]
\end{aligned}$
Dimensions of $\mathrm{NmK}^{-1}$ is
$\begin{aligned}
& =\left[\mathrm{MLT}^{-2}\right][\mathrm{L}][\mathrm{K}]^{-1} \\
& =\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]
\end{aligned}$
Dimensions of $\mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$
$\begin{aligned}
& =\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right][\mathrm{M}]^{-1}[\mathrm{~K}]^{-1} \\
& =\left[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]
\end{aligned}$
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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