More practice questions

4. Q4. The average translational kinetic energy of a gas molecule is (3/2)k_BT, where T is the absolute temperature. Find the dimensional formula of the Boltzmann constant k_B.

   Show answerHide answer

   k_B = (2/3)E/T, and 2/3 is a pure number. [k_B] = [M L^² T^⁻²]/[K] = [M L^² T^⁻² K^⁻¹].

5. Q5. A charge q moving with speed v at right angles to a magnetic field B feels a force F = qvB. Find the dimensional formula of B.

   Show answerHide answer

   B = F/(qv). [B] = [M L T^⁻²]/([A T][L T^⁻¹]) = [M L T^⁻²]/[A L] = [M T^⁻² A^⁻¹].

6. Q6. In Coulomb’s law, F = q₁q₂/(4πε₀r^²). Find the dimensional formula of ε₀.

   Show answerHide answer

   ε₀ = q₁q₂/(4πFr^²), and 4π is a pure number. [ε₀] = [A T]^²/([M L T^⁻²][L^²]) = [A^² T^²]/[M L^³ T^⁻²] = [M^⁻¹ L^⁻³ T^⁴ A^²].