Match List I with List II
List-I List-II
A Spring constant I $[T^{- 1}]$
B Angular speed II $[M T^{- 2}]$
C Angular momentum III $[M L^{2}]$
D Moment of Inertia IV $[M L^{2} T^{- 1}]$
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Question

Match List I with List II

	List-I		List-II
A	Spring constant	I	$[T^{- 1}]$
B	Angular speed	II	$[M T^{- 2}]$
C	Angular momentum	III	$[M L^{2}]$
D	Moment of Inertia	IV	$[M L^{2} T^{- 1}]$

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TestHub · Accepted Answer

The formula to calculate the spring constant is
$F = k x . . . (1)$
The formula to calculate the angular speed is
$ω = \frac{2 π}{T} . . . (2)$
The formula to calculate the angular momentum is
$L = m v r . . . (3)$
The formula to calculate the moment of inertia is
$I = M R^{2} . . . (4)$
Use the method of dimensional analysis to obtain the dimensions of the required quantities. From above relations, we can write
$\begin{array}{rcl} [M L T^{- 2}] & = & [k] [L] \\ \Rightarrow & [k] = [M T^{- 2}] \\ [ω] & = & \frac{1}{[T]} \\ = & [T^{- 1}] \\ [L] & = & [M] [L T^{- 1}] [L] \\ = & [M L^{2} T^{- 1}] \\ [I] & = & [M] [L^{2}] \\ = & [M L^{2}] \end{array}$

Physics - Unit & Dimension Question with Solution | TestHub

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