Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Units and Dimensions

NTA Abhyas 2020 · Physics · Units and Dimensions

If speed V , force F and acceleration a are chosen as the...

If speed VV, force FF and acceleration aa are chosen as the fundamental physical quantities, then the dimension of Young's modulus in terms of VV, FF and aa& are

Options

  1. A[V−3Fa]\left[V^{- 3}Fa\right]
  2. B[V−4F2a2]\left[V^{- 4}F^{2}a^{2}\right]
  3. C[V−4Fa2]\left[V^{- 4}{Fa}^{2}\right]
  4. D[V−4F2a]\left[V^{- 4}F^{2}a\right]

Correct answer

C. [V−4Fa2]\left[V^{- 4}{Fa}^{2}\right]

Step-by-step solution

Let Y=f(V,F,a)Y = f \left(V, F, a\right)

∴Y=KVxFyaz,K→∴ Y = {KV}^{x}F^{y}a^{z}, K \to Unitless

∴[Y]=[V]x[F]∴ \left[Y\right] = \left[V\right]x\left[F\right] y\left[a\right]zz

∴[ML−1T−2]=∴ \left[{ML}^{- 1}T^{- 2}\right] =\left[{LT}^{- 1}\rright]x\left[{MLT}^{- 2}\rright]y\left[{LT}^{- 2}\right]zz

∴[M][L−1]=[T−2]=[M]y[Lx+y+z][T−x−2y−2z]∴ \left[M\right]\left[L^{- 1}\right] = \left[T^{- 2}\right]{=}^{ } \left[M\right]y\left[L^{x + y + z}\right]\left[T^{- x - 2y - 2z}\right]

∴y=1;x+y+z=−1;−x−2y−2z=2∴ y = 1; x + y + z = - 1; - x - 2y - 2z = 2

∴x+z=−2∴x+2y+2z=2∴ x + z = - 2 ∴ x + 2y + 2z = 2

∴x+2z=0∴ x + 2z = 0 & & & ∴z=2,x=−4∴ z = 2, x = - 4

∴[Y]=[V−4Fa2]∴ \left[Y\right] = \left[V^{- 4}{Fa}^{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 NTA Abhyas JEE Main PYQs