Tag: physics

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Multiple choice standardized measurement measurement of physical quantities need of unit for measurement measurements and experimentation physics

The wavelength of light is expressed in

  1. Metre

  2. Micron

  3. Light year

  4. Angstrom
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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.

Multiple choice standardized measurement measurement of physical quantities need of unit for measurement measurements and experimentation physics

If the displacement, velocity and acceleration of a particle at time t be x, v and f respectively, then which one is true?

  1. $f=v^3\dfrac{d^2t}{dx^2}$

  2. $f=-v^3\dfrac{d^2t}{dx^2}$

  3. $f=v^2\dfrac{d^2t}{dx^2}$

  4. $f=-v^2\dfrac{d^2t}{dx^2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We know that the velocity can be written as:
$v=\dfrac{dx}{dt}$

Therefore, $\dfrac1v=\dfrac{dt}{dx}$

Now, expressing $f$ in terms of velocity.

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

Multiple choice standardized measurement measurement of physical quantities need of unit for measurement measurements and experimentation physics

Which of the following pairs has not the same dimension?

  1. Stress; pressure

  2. Force; surface tension

  3. Impulse; linear momentum

  4. Frequency; angular velocity
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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.

Multiple choice standardized measurement measurement of physical quantities need of unit for measurement measurements and experimentation physics

The force F is given in terms of time t and displacement x by the equation F = A cosBx + C sin Dt. The dimensional formula of D/B is______

  1. $[M^oL^oT^o]$

  2. $[M^oL^o{T}^{-1}]$

  3. $[M^o{L}^{-1}T^o]$

  4. $[M^o{L}^{1} {T}^{-1}]$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$F = A\ cosBx + C\ sinDt$

the argument, $\theta $ of cos or sin should be dimensionless.
therefore,
dimension of Bx = $[MLT]$
$[B] [L'] = [MLT]$

$[B] = [M{L}^{0}T]$

Similarly $[D][T'] = [MLT]$
$[D] = [ML{T}^{0}$
dimension of $DB=\dfrac{[ML{T}^{0}]}{[ML^0T]}$
= $[L^1{T}^{-1}]$

Multiple choice standardized measurement measurement of physical quantities need of unit for measurement measurements and experimentation physics

Which of the following conversions is correct?

  1. 1 atm = 1.01 x 10$^4$ Pa

  2. 1 mm of Hg = 133 Pa

  3. 1 bar = 10$^7$ Pa

  4. 1 torr = 10$^2$ Pa
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

 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. $1 mm Hg =133.322387415 \ pascal$.

Multiple choice physics reflection of light and shadow beam of light ray and beam ray optics

Which of the following is correct for the beam which enters the medium ? 

  1. Travel as a cylindrical beam

  2. Diverge

  3. Converge

  4. Diverge near the axis and converge near the periphery
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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.