Physics · Science General

Units and Measurement

1,044 Questions

Master the fundamentals of physics with these practice questions on units and measurement. The topics include fundamental SI units, derived quantities, and specific units for power, force, and light. These questions are essential for building a strong foundation for competitive exams.

SI fundamental unitsUnits of powerDerived quantities unitsThermal energy unitsVolume measurement unitsElectric current units

Units and Measurement Questions

Multiple choice physics measurements and experimentation measuring distance of celestial bodies unconventional units of measurements units of mass

In which of the following lists are the units an order from LONGEST to SHORTEST?

  1. light-year, kilometer, astronomical unit

  2. astronomical unit, kilometer, light-year

  3. kilometer, light-year, astronomical unit

  4. light-year, astronomical unit, kilometer
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$1$ Light year $=9.461\times 10^{15}\,m$


$1$ Astronomical unit $=1.496\times 10^{11}\,m$

$1$ kilometer $=1000\,m$

Socorrect answer is option (D).

Multiple choice physics measurement and effects of heat heat exchange calorimeter measuring thermal quantities by the method of mixtures

The quantity/ quantities that does/do not have mass in its/their dimensions is/are

  1. Specific heat

  2. Latent heat

  3. Electrical potential difference

  4. Electrical resistance
Reveal answer Fill a bubble to check yourself
C,D Correct answer
Explanation

Specific heat- $J/kg^oC$
Latent Heat- J/kg
Electrical potential difference- J/coulumb
Electrical resistance- ohm
 Hence, option C and D are correct

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

In an experimental set up, the density of a small sphere is to be determined. The diameter of the small sphere is measured with the help of a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the sphere has a relative error of 2%, the relative percentage error in the density is

  1. $0.03$%
  2. $3.11$%
  3. $0.08$%
  4. $8.2$%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

First find the least count of the screw gauge, which is pitch/divisions = 0.5 mm / 50 = 0.01 mm. The measured diameter is main scale reading + circular scale reading * least count = 2.5 mm + 20 * 0.01 mm = 2.7 mm. The relative error in diameter is least count / measured diameter, and the relative error in density (mass / volume) combines mass error and three times the diameter error.

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

The heat generated in a circuit is dependent on the resistance, current and time of flow of electric current. If the percentage errors measured in the above physical quantities are 1%, 2% and 1% respectively, the maximum error in measuring the heat is :

  1. $2\%$
  2. $3\%$
  3. $6\%$
  4. $1\%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation


$ H={ I }^{ 2 }RT$ (by dimensional analysis)
$\displaystyle \frac { \triangle n }{ n } =(2\frac { \triangle I }{ I } +\frac { \triangle R }{ R } +\frac { \triangle T }{ T } )$%
          $=2(2)+1+1$
          $= 6 $ %

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

The heat generated in a circuit is dependent upon the resistance, current and time for which the current is flown. If the error in measuring the above are 1%, 2% and 1% respectively. The maximum error in measuring the heat is :

  1. 8%

  2. 6%

  3. 18%

  4. 12%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$ Q = I^2 R t$


$ \dfrac{\delta Q}{ Q }= 2\dfrac{\delta i}{i}+ \dfrac{\delta R}{R}+\dfrac{\delta t}{t}$

$ \dfrac{\delta Q}{ Q }= 2\times 2$ % $+ 1$%$+1$%

$ \dfrac{\delta Q}{ Q }=6$ % 

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

The length and breadth of a rectangular object are 25.2 cm and 16.8 cm respectively and have been measured to an accuracy of 0.1 cm. The relative error and percentage error in the area of the object are:

  1. 0.01 ; 1%

  2. 0.1 ; 10%

  3. 1 ; 10 %

  4. 1 ; 100 %
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$Area  = l\times b$

$\dfrac { \triangle A }{ A } =\dfrac { \triangle l }{ l } +\dfrac { \triangle b }{ b }$


           $ = (\dfrac{0.1}{25.2} + \dfrac{0.1}{16.8})=0.00992\approx0.01$


This is the relative error.

Percentage  error $ =  0.01 \times 100  =  1\%$

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

In a measurement, the uncertainty of length $L$ is $\pm a$ and the uncertainty of width $W$ is $\pm b$. Assuming a and b very small, find the the uncertainty in measurement of area. 

  1. $a/L+b/W$
  2. $aL+bW$
  3. $aW+bL$
  4. $a^2/W+b^2/L$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Here given, $\Delta L=a$ and $\Delta W=b$
Area, $A=LW$
Take ln and then differentiate, $\dfrac{\Delta A}{A}=\dfrac{\Delta L}{L}+\dfrac{\Delta W}{W}=a/L+b/W$
So,$\Delta A=(a/L+b/W)(LW)=aW+bL$

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

In an experiment, the value of refractive index of a plastic has been found 1.33,1.30, 1.34 and 1.29 in successive measurements. Find the mean absolute error for refractive index.  

  1. $0.12$
  2. $0.02$
  3. $0.10$
  4. $0.01$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Here the mean value, $\bar{n}=\dfrac{1.33+1.30+1.34+1.29}{4}=1.31$
The absolute error in each measurements are, 
$\Delta n _1=\bar{n}-n _1=1.31-1.33=-0.02$;
$\Delta n _2=\bar{n}-n _2=1.31-1.30=0.01$;
$\Delta n _3=\bar{n}-n _3=1.31-1.34=-0.03$;
$\Delta n _4=\bar{n}-n _4=1.31-1.29=0.02$;
The mean absolute error, $\Delta \bar{n}=\dfrac{|\Delta n _1|+|\Delta n _2|+|\Delta n _3|+|\Delta n _4|}{4}=\dfrac{0.02+0.01+0.03+0.02}{4}=0.02$

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

The energy of a system as a function of time t is given as $E(t) = A^2 exp(- \alpha t)$, where $\alpha = 0.2 s^{-1}$. The measurement of A has an error of 1.25%. If the error in the measurement of time is 1.50%, the percentage error in the value of $E(t)$ at t = 5 s is:

  1. 2%

  2. 4%

  3. 3%

  4. 5%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$E(t) = A^2 e^{-\alpha t}$
Taking natural logarithm on both sides,
$ln(E) = 2ln(A) + (- \alpha t)$
Differentiating both sides
$\displaystyle \frac{dE}{E} = 2\frac{dA}{A} + (\alpha dt)$
Errors always add up for maximum error.
$\displaystyle \therefore \frac{dE}{E} = 2\frac{dA}{A} + \alpha \left( \frac{dt}{t} \right) \times t$
Here, $\displaystyle \frac{dA}{A} = 1.25$ %, $\displaystyle \frac{dt}{t} = 1.5$%, $t = 5s$, $\displaystyle \alpha = 0.2 s^{-1}$
$\therefore \displaystyle \frac{dE}{E} = (2 \times 1.25$%$\displaystyle ) + (0.2) \times (1.5$%$) \times 5 = 4$%