Units and Measurements

Topics in this chapter

• Measurement Systems and Derived Units
• Dimensional Analysis and Formulae
• Measuring Instruments and Least Count
• Errors and Error Propagation
• Significant Figures and Rounding

Cheat sheet

Practice questions

1. Question 1Q-A15CAD

   The dimensional formula of the universal gravitational constant $G$ is:

   1. A.$[M^{-1} L^3 T^{-2}]$
   2. B.$[M L^2 T^{-2}]$
   3. C.$[M^{-1} L^2 T^{-2}]$
   4. D.$[M L^3 T^{-2}]$
   See the answer and solution
2. Question 2Q-393ED9

   If energy ($E$), velocity ($v$), and time ($T$) are chosen as the fundamental physical quantities, the dimensional formula for surface tension will be:

   1. A.$[E v^{-2} T^{-2}]$
   2. B.$[E v^{-1} T^{-2}]$
   3. C.$[E v^{-2} T^{-1}]$
   4. D.$[E^2 v^{-1} T^{-2}]$
   See the answer and solution
3. Question 3Q-664730

   In an experiment, the percentage errors incurred in the measurement of mass and velocity are $1\%$ and $2\%$ respectively. The maximum percentage error in the measurement of kinetic energy is:

   1. A.$3\%$
   2. B.$5\%$
   3. C.$2\%$
   4. D.$4%"
   See the answer and solution
4. Question 4Q-0B31E2

   The length of a cylinder is measured with a meter rod having least count $0.1\text{ cm}$. Its diameter is measured with vernier calipers having least count $0.01\text{ cm}$. Given that length $L = 5.0\text{ cm}$ and radius $R = 2.0\text{ cm}$, the percentage error in the calculated volume of the cylinder is approximately:

   1. A.$1.5\%$
   2. B.$2.5\%$
   3. C.$3.0\%$
   4. D.$1.0%"
   See the answer and solution
5. Question 5Q-B279B8

   Which of the following sets of physical quantities has the same dimensions?

   1. A.Planck's constant, angular momentum, and torque
   2. B.Work, torque, and energy
   3. C.Pressure, stress, and strain
   4. D.Velocity, momentum, and impulse
   See the answer and solution