Tag: measurements and experimentation

Questions Related to measurements and experimentation

Which of the following pairs has not the same dimension?

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

  1. Stress; pressure

  2. Force; surface tension

  3. Impulse; linear momentum

  4. Frequency; angular velocity

Show answer
Correct Option: B
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.

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______

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

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

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

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

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

Show answer
Correct Option: D
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 $DB=\dfrac{[ML{T}^{0}]}{[ML^0T]}$
= $[L^1{T}^{-1}]$

Which of the following conversions is correct?

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

  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

Show answer
Correct Option: B
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. $1 mm Hg =133.322387415 \ pascal$.

The CGS unit of power is $erg\ s^{-1}$

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

  1. True

  2. False

Show answer
Correct Option: A
Explanation:
Power is defined as the rate of doing work.
CGS unit of power is $erg \ s^{-1}$

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

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

  1. True

  2. False

Show answer
Correct Option: B
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.

The ratio of S.I. unit of thrust to the C.G.S unit of force is $10^5 : 1$

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

  1. True

  2. False

Show answer
Correct Option: A
Explanation:
S.I. unit of thrust (or force) is Newton  $(N)$ and C.G.S. unit is $dyne$.
We know that  $1 = N = 10^5 \ dynes$
Ratio of S.I. unit of force to C.G.S. unit is   $N:dyne = 10^5 :1$

The MKS unit of force is N.

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

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

MKS unit of force is $kg \ m/s^2$ which is also expressed as Newton. Thus the above statement is true.

Dynes $cm^{-2}$ is the CGS unit of pressure.

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

  1. True

  2. False

Show answer
Correct Option: A
Explanation:
Pressure is defined as the force acting on the surface per unit its area.
CGS unit of pressure is  $dynes \ cm^{-2}$

Find the SI unit of the following derived quantities :

Pressure

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

  1. Pascal

  2. Newton

  3. Kg

  4. length

Show answer
Correct Option: A
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.

The C.G.S unit of speed is:

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

  1. cm/g

  2. m/s

  3. m/g

  4. cm/s

Show answer
Correct Option: D
Explanation:

The C.G.S. unit of speed is $ cm/s$.

C.G.S. units stand for centimetre–gram–second system of units.