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1.Units, Dimensions and Measurement
medium
$Pascal-Second$ has dimension of
AForce
BEnergy
CPressure
DCoefficient of viscosity
Solution
Pascal is unit of pressure, hence its dimensional formula is
$\left[M L^{-1} T^{-2}\right]$
$\therefore$ Dimensional formula of Pascal-second is $\left[M L^{-1} T^{-1}\right]$
By the formula of coefficient of viscosity, we have
$\eta=\frac{F}{A(\Delta v / \Delta z)}$
where $F$ is force, $A$ is area and $\frac{\Delta v}{\Delta z}$ is velocity gradient.
$\therefore$ Dimensions of $\eta=\frac{\left[M L T^{-2}\right]}{\left[L^{2}\right]\left[L T^{-1} / L\right]}$
$=\left[M L^{-1} T^{-1}\right]$
Hence, Pascal-second has dimensions of coefficient of viscosity.
$\left[M L^{-1} T^{-2}\right]$
$\therefore$ Dimensional formula of Pascal-second is $\left[M L^{-1} T^{-1}\right]$
By the formula of coefficient of viscosity, we have
$\eta=\frac{F}{A(\Delta v / \Delta z)}$
where $F$ is force, $A$ is area and $\frac{\Delta v}{\Delta z}$ is velocity gradient.
$\therefore$ Dimensions of $\eta=\frac{\left[M L T^{-2}\right]}{\left[L^{2}\right]\left[L T^{-1} / L\right]}$
$=\left[M L^{-1} T^{-1}\right]$
Hence, Pascal-second has dimensions of coefficient of viscosity.
Standard 11
Physics
Similar Questions
Match List$-I$ with List$-II.$
| List$-I$ | List$-II$ |
| $(a)$ Capacitance, $C$ | $(i)$ ${M}^{1} {L}^{1} {T}^{-3} {A}^{-1}$ |
| $(b)$ Permittivity of free space, $\varepsilon_{0}$ | $(ii)$ ${M}^{-1} {L}^{-3} {T}^{4} {A}^{2}$ |
| $(c)$ Permeability of free space, $\mu_{0}$ | $(iii)$ ${M}^{-1} L^{-2} T^{4} A^{2}$ |
| $(d)$ Electric field, $E$ | $(iv)$ ${M}^{1} {L}^{1} {T}^{-2} {A}^{-2}$ |
