SI units; fundamental and derived units — practice questions

Question 1 · difficulty L2 · understanding

A new unit ( $\alpha$ ) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of $\alpha$ units if light takes 6 min. 40 s to cover this distance?

• A. $200 \alpha$
• B. $400 \alpha$
• C. $300 \alpha$
• D. $500 \alpha$

Question 2 · difficulty L2 · understanding

If $\epsilon, E$ and $t$ represent the free space permittivity, electric field and time respectively, then the unit of $\frac{\epsilon E}{t}$ will be :

• A. Am
• B. $\mathrm{A} / \mathrm{m}$
• C. $\mathrm{A} / \mathrm{m}^2$
• D. $\mathrm{Am}^2$

Question 3 · difficulty L2 · understanding

$$\text { Match the LIST-I with LIST-II }$$ LIST-I LIST-II A. $$\text { Boltzmann constant }$$ I $$\mathrm{ML}^2 \mathrm{~T}^{-1}$$ B $$\text { Coefficient of viscosity }$$ II $$\mathrm{MLT}^{-3} \mathrm{~K}^{-1}$$ C $$\text { Planck's constant }$$ III $$\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}$$ D $$\text { Thermal conductivity }$$ IV $$\mathrm{ML}^{-1} \mathrm{~T}^{-1}$$ Choose the correct answer from the options given below:

• A. A - III, B - IV, C - I, D - II
• B. A - III, B - IV, C - II, D - I
• C. A - III, B - II, C - I, D - IV
• D. A - II, B - III, C - IV, D - I

Question 4 · difficulty L2 · understanding

In an expression $$a \times 10^b$$ :

• A. $$a$$ is order of magnitude for $$b \leq 5$$
• B. $$b$$ is order of magnitude for $$a \leq 5$$
• C. $$b$$ is order of magnitude for $$a \geq 5$$
• D. $$b$$ is order of magnitude for $$5< a \leq 10$$

Question 5 · difficulty L2 · understanding

Match List I with List II LIST I LIST II A. Spring constant I. $$\mathrm{[T^{-1}]}$$ B. Angular speed II. $$\mathrm{[MT^{-2}]}$$ C. Angular momentum III. $$\mathrm{[ML^2]}$$ D. Moment of inertia IV. $$\mathrm{[ML^2T^{-1}]}$$ Choose the correct answer from the options given below:

• A. A-IV, B-I, C-III, D-II
• B. A-II, B-III, C-I, D-IV
• C. A-II, B-I, C-IV, D-III
• D. A-I, B-III, C-II, D-IV

Question 6 · difficulty L2 · understanding

Given below are two statements : Statements I : Astronomical unit (Au), Parsec (Pc) and Light year (ly) are units for measuring astronomical distances. Statements II : $$\mathrm{Au} < \mathrm{Parsec} (\mathrm{Pc}) < \mathrm{ly}$$ In the light of the above statements, choose the most appropriate answer from the options given below:

• A. Both Statements I and Statements II are incorrect.
• B. Both Statements I and Statements II are correct,
• C. Statements I is incorrect but Statements II is correct.
• D. Statements I is correct but Statements II is incorrect.

Question 7 · difficulty L2 · understanding

Match List I with List II LIST I LIST II A. Torque I. $$\mathrm{ML^{-2}T^{-2}}$$ B. Stress II. $$\mathrm{ML^2T^{-2}}$$ C. Pressure gradient III. $$\mathrm{ML^{-1}T^{-1}}$$ D. Coefficient of viscosity IV. $$\mathrm{ML^{-1}T^{-2}}$$ Choose the correct answer from the options given below:

• A. A-II, B-I, C-IV, D-III
• B. A-II, B-IV, C-I, D-III
• C. A-IV, B-II, C-III, D-I
• D. A-III, B-IV, C-I, D-II

Question 8 · difficulty L2 · understanding

Match List I with List II : List I List II A. Torque I. $\mathrm{kg} \mathrm{m}^{-1} \mathrm{~s}^{-2}$ B. Energy density II. $\mathrm{kg} \,\mathrm{ms}^{-1}$ C. Pressure gradient III. $\mathrm{kg}\, \mathrm{m}^{-2} \mathrm{~s}^{-2}$ D. Impulse IV. $\mathrm{kg} \,\mathrm{m}^{2} \mathrm{~s}^{-2}$ Choose the correct answer from the options given below:

• A. A-IV, B-I, C-III, D-II
• B. A-IV, B-I, C-II, D-III
• C. A-I, B-IV, C-III, D-II
• D. A-IV, B-III, C-I, D-II

Question 9 · difficulty L2 · understanding

Match List I with List II. List I List II A. Torque I. Nms$$^{ - 1}$$ B. Stress II. J kg$$^{ - 1}$$ C. Latent Heat III. Nm D. Power IV. Nm$$^{ - 2}$$ Choose the correct answer from the options given below :

• A. A-III, B-II, C-I, D-IV
• B. A-III, B-IV, C-II, D-I
• C. A-IV, B-I, C-III, D-II
• D. A-II, B-III, C-I, D-IV

Question 10 · difficulty L2 · understanding

Match List - I with List - II. List - I List - II (a) $${R_H}$$ (Rydberg constant) (i) $$kg\,{m^{ - 1}}{s^{ - 1}}$$ (b) h (Planck's constant) (ii) $$kg\,{m^2}{s^{ - 1}}$$ (c) $${\mu _B}$$ (Magnetic field energy density) (iii) $$\,{m^{ - 1}}$$ (d) $$\eta$$ (coefficient of viscocity) (iv) $$kg\,{m^{ - 1}}{s^{ - 2}}$$ Choose the most appropriate answer from the options given below :

• A. (a)-(ii), (b)-(iii), (c)-(iv), (d)-(i)
• B. (a)-(iii), (b)-(ii), (c)-(iv), (d)-(i)
• C. (a)-(iv), (b)-(ii), (c)-(i), (d)-(iii)
• D. (a)-(iii), (b)-(ii), (c)-(i), (d)-(iv)