Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20245 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
5 April
Shift
Evening Shift
Subject
Physics
Chapter
Units and Dimensions

JEE Main 2024 · 5 April · Evening Shift · Physics · Units and Dimensions

What is the dimensional formula of a b^ -1 in the equation (P+ a...

What is the dimensional formula of ab−1intheequation(P+aV2)(V−b)=RTa b^{-1} in the equation \left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}, where letters have their usual meaning.

Options

  1. A[M−1 L5 T3]\left[\mathrm{M}^{-1} \mathrm{~L}^5 \mathrm{~T}^3\right]
  2. B[M6 L7 T4]\left[\mathrm{M}^6 \mathrm{~L}^7 \mathrm{~T}^4\right]
  3. C[ML2 T−2]\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]
  4. D[M0 L3 T−2]\left[\mathrm{M}^0 \mathrm{~L}^3 \mathrm{~T}^{-2}\right]

Correct answer

C. [ML2 T−2]\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]

Step-by-step solution

\because[\mathrm{V}]=[\mathrm{b}] \thereforeDimensionofDimension ofb=\left[\mathrm{L}^3\right] [P]=[aV2][a]=[PV2]=[ML−1 T−2][L6]\begin{aligned} & &[\mathrm{P}]=\left[\frac{\mathrm{a}}{\mathrm{V}^2}\right] \\ & {[\mathrm{a}]=\left[\mathrm{PV}^2\right]=\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]\left[\mathrm{L}^6\right]} \end{aligned}DimensionofDimension of\mathrm{a}=\left[\mathrm{ML}^5 \mathrm{~T}^{-2}\right] \therefore \mathrm{ab}^{-1}=\frac{\left[\mathrm{ML}^5 \mathrm{~T}^{-2}\right]}{\left[\mathrm{L}^3\right]}=\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]
Practice Units and Dimensions on Quantrex Academy →

More from Units and Dimensions

In a new system of units, the units of mass, length, time and current are 5 kg, 5 m, 5 s… JEE Advanced 2026A new unit (α) of length is chosen such that it is equal to the speed of light in vacuum.… JEE Main 2026Consider the equation H = (x^p ε^q E^r)/(t^s) , where H= magnetic field; E= electric… JEE Main 2026The percentage error in the calculated volume of a sphere, if there is 2\% error in its… JEE Main 2026Match List - I with List - II. List - I List - II A. Boltzmann constant I. [M^ -1 L^3T^… JEE Main 2026The potential energy of a particle changes with distance x from a fixed origin as V = A x… JEE Main 2026Match List-I with List-II. List-I List-II A. Meter (L) I. (hc)/(G) B. Second (S) II.… JEE Main 2026L , C and R represents physical quantities inductance, capacitance and resistance… JEE Main 2026 Full Units and Dimensions list All JEE Main PYQs