Question

Assertion : Pressure has the dimensions of energy density. Reason : Energy density = ("energy")/("volume")=(["ML"^(2)"T"^(-2)])/(["L"^(3)]) =["ML"^(-1)"T"^(-2)]="pressure"

Answer 1

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{Yes, \red{ True.}} \\ \\ </p><p></p><p> \: \: \tt{[Pressure= \frac{Energy}{ Volume}.]}$

$\tt{{Pressure} = \frac{ Force}{ Area}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \tt{ \frac{{M }^{1} {L}^{1}{ T}^{ - 2} }{ {L }^{2} }}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \tt{ {M }^{1} {L}^{ - 1}{ T}^{ - 2} }.$

$\tt{ \frac{ Energy }{Volume} = \frac{ Force \times displacement} {L \times L \times L}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \tt{= \frac{ {M}^{1} {L }^{1} {T }^{ - 2} \times L}{ L \times L \times L}}$

$\: \: \: \: \: \: \: \: \: \: \: \: = \tt{ {M }^{1} {L}^{ - 1}{ T}^{ - 2} }.$

$\tt{We \: can \: say \: that,}$

$\tt{ \large{[ } \frac{ Energy}{ Volume} = \underline {Pressure}.}$