Match List I with List II List-I List-II A Spring constant I [ T ^...

The formula to calculate the spring constant is

$F = kx . . . \left(1\right)$

The formula to calculate the angular speed is

$\omega = \dfrac{2\pi}{T} . . . \left(2\right)$

The formula to calculate the angular momentum is

$L = mvr . . . ( 3 )$

The formula to calculate the moment of inertia is

$I = M{R}^{2} . . . \left(4\right)$

Use the method of dimensional analysis to obtain the dimensions of the required quantities. From above relations, we can write

$\begin{cases}\left[ML{T}^{- 2}\right] & = & \left[k\right]\left[L\right] \\ & ⇒ & \left[k\right] = \left[M{T}^{- 2}\right] \\ & & \\ \left[\omega\right] & = & \dfrac{1}{\left[T\right]} \\ & = & \left[{T}^{- 1}\right] \\ & & \\ \left[L\right] & = & \left[M\right]\left[L{T}^{- 1}\right]\left[L\right] \\ & = & \left[M{L}^{2}{T}^{- 1}\right] \\ & & \\ \left[I\right] & = & \left[M\right]\left[{L}^{2}\right] \\ & = & \left[M{L}^{2}\right]\end{cases}$