$Statement$ $(I)$ : Planck's constant and angular momentum have same dimensions.
$Statement$ $(II)$ : Linear momentum and moment of force have same dimensions.
In the light of the above statements, choose the correct answer from the options given below :
$ {[\mathrm{~L}]=\mathrm{ML}^2 \mathrm{~T}^{-1}} $
$ {[\mathrm{P}]=\mathrm{MLT}^{-1}} $
$ {[\tau]=\mathrm{ML}^2 \mathrm{~T}^{-2}}$
(Here $\mathrm{h}$ is Planck's constant, $\mathrm{L}$ is angular momentum, $\mathrm{P}$ is linear momentum and $\tau$ is moment of force)
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[Given: The acceleration due to gravity $g=10 \mathrm{~ms}^{-2}$ and $\pi=3.14$ ]
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($1$) Considering the air flow to be streamline, the steady mass flow rate of air exiting the chimney is
. . . . .$\mathrm{gm} \mathrm{s}^{-1}$.
($2$) When the chimney is closed using a cap at the top, a pressure difference $\Delta P$ develops between the top and the bottom surfaces of the cap. If the changes in the temperature and density of the hot air, due to the stoppage of air flow, are negligible then the value of $\Delta P$ is. . . . .$\mathrm{Nm}^{-2}$.
