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Question: Answered & Verified by Expert
The pair of quantities having same dimensions is:
PhysicsUnits and DimensionsNEETNEET 2013 (Karnataka)
Options:
  • A Impulse and Surface Tension
  • B Angular momentum and Work
  • C Work and Torque
  • D Young's modulus and Energy
Solution:
1052 Upvotes Verified Answer
The correct answer is: Work and Torque
(1)
$$
\begin{aligned}
\text { Torque }=\text { F.S. } & =\left[\mathrm{MLT}^{-2}\right][\mathrm{L}] \\
& =\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]
\end{aligned}
$$
correct option is (3)
(2) Angular moment $=$ M.I. $\times$ angular velocity
$$
\begin{aligned}
=\left[\mathrm{ML}^2\right]\left[\mathrm{T}^{-1}\right] & =\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right] \\
\text { Work }=F . S . & =\left[\mathrm{MLT}^{-2}\right][\mathrm{L}] \\
& =\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]
\end{aligned}
$$
(3) Work $=\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]$ from
Related Theory
(1)
$$
\begin{aligned}
& \text { Impluse }=\text { force } \times \text { time } \\
&=\left[M L T^{-2}\right][T]=\left[M L T^{-1}\right] \\
& \text { Surface tension }=\frac{\text { Force }}{\text { length }}= \\
& \frac{\left[M L T^{-2}\right]}{[L]}=\left[M T^{-1}\right]
\end{aligned}
$$

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