Tag: need of unit for measurement

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

The ratio of the C.G.S unit of pressure to the S.I unit of pressure is 10.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
SI unit of pressure is $N/m^2$ and CGS unit of pressure is $dyne/cm^2$.
We know that  $1 \ N = 10^5 \ dyne$  and   $1 \ m  =10^0 \ cm$
ratio of CGS unit to SI unit  $\dfrac{1 \ dyne/cm^2}{N/m^2} = \dfrac{1 \ dyne/cm^2}{10^5 \ dyne/(100)^2 \ cm^2} = \dfrac{1}{10} $
Thus the given statement is false.
Multiple choice standardized measurement measurement of physical quantities need of unit for measurement measurements and experimentation physics

Find the SI unit of the following derived quantities :

Pressure

  1. Pascal

  2. Newton

  3. Kg

  4. length
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given pressure $\displaystyle = \frac{Force}{Area}$
$\therefore$ MKS unit of pressure $\displaystyle = \frac{S.I.  unit \ of \   force}{S.I.  unit \ of \ area} = \frac{kg  m  s^{-2}}{m^2}$
$\displaystyle = \frac{kg.m}{m^2 . s^2} = \frac{kg}{m.s^2}$
$\therefore$ MKS unit of pressure $= kg m^{-1} s^{-2}$
SI unit of pressure is pascal.