Tag: physics

Gas equation,
$PV=nRT$

SI unit of amplitude of oscillation is metre  $(m)$

Angstrom $(\dot A)$ unit of length used chiefly in measuring wavelengths of light, equal to $10^{-10}$ metre, or $0.1$ nanometer.  It is used to express wavelengths of visible light, ultraviolet (UV) light, X rays, and gamma rays.

SI unit of mass is kilogram i.e.  $Kg$.
Thus the above statement is false.

$\dfrac{d^2t}{dx^2}=\dfrac{d\begin{pmatrix}\dfrac{dt}{dx}\end{pmatrix}}{dx}=\dfrac{d\begin{pmatrix}\frac{1}{v}\end{pmatrix}}{dx}=-\dfrac{1}{v^2}\dfrac{dv}{dt}\times\dfrac{1}{v}$
$\Rightarrow\;f=-v^3\dfrac{d^2t}{dx^2}$

A unit is said to be a standard unit of does not change with respect to space and time.

Surface Tension$ (T) =\dfrac{ Force}{Length}$  . . . . . (1)

Since, $Force = Mass \times Acceleration$

And, $Acceleration = \dfrac{velocity}{ time}= [L T^{-2}]$

$\therefore $ The dimensional formula of force $= M^1L^1T^{-2}$ . . . . (2)

On substituting equation (2) in equation (1) we get,

Surface Tension $(T) = \dfrac{Force}{  Length}$

Or, $T=\dfrac{[M^1L^1T^{-2}]}{[L^{1}]}=M^1T^{-2}$ 

Therefore, surface tension is dimensionally represented as $[M^1T^{-2}]$

Dimension of force $=M^1L^1T^{-2}$

So the dimension of force and surface tension are different.

$F = A\ cosBx + C\ sinDt$

 The answer is $0.0075006157584566$. We assume you are converting between and pascal. You can view more details on each measurement unit: mm Hg or pascal The SI derived unit for pressure is the pascal. $1 mm Hg =133.322387415 \ pascal$.

Since the refractive index is less at beam boundary, the ray at the edges of the beam move faster compared to the axis of beam. Hence the beam converges.