Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JIPMER 2006
Exam
JIPMER
Year
2006
Subject
Physics
Chapter
Units and Dimensions

JIPMER 2006 · Physics · Units and Dimensions

In a system of units if force (F) , acceleration (A) , and time ( T...

In a system of units if force (F)(F), acceleration (A)(A), and time ( TT ) are taken as fundamental units, then the dimensional formula of energy is :

Options

  1. AFA2TF A^2 T
  2. BFAT2F A T^2
  3. CF2ATF^2 A T
  4. DFAT

Correct answer

B. FAT2F A T^2

Step-by-step solution

Let energy E=FxAyT3E=F^x A^y T^3 Writing the dimensions on both sides [ML2T−2]=[ MLT −2]x[ LT −2]y[T]2[ML2T−2]=[MxLx+yT−2x−2y+z]\begin{aligned} & {\left[\mathrm{ML}^2 \mathrm{ T}^{-2}\right]=\left[\mathrm{\text{ MLT }}^{-2}\right]^x\left[\mathrm{\text{ LT }}^{-2}\right]^y[\mathrm{ T}]^2} \\ & {\left[\mathrm{ML}^2 \mathrm{ T}^{-2}\right]=\left[\mathrm{M}^x \mathrm{ L}^{x+y} \mathrm{ T}^{-2 x-2 y+z}\right]}\end{aligned} On comparing both sides x=1x+y=2⇒y=2−x=2−1=1 and −2x−2y+z=−2⇒−2×1−2×1+z=−2⇒z=−2+2+2=2\begin{aligned} & x=1 \\ & x+y=2 \\ & \Rightarrow \quad y=2-x=2-1=1 \\ & \text{ and } \quad-2 x-2 y+z=-2 \\ & \Rightarrow-2 \times 1-2 \times 1+z=-2 \\ & \Rightarrow \quad z=-2+2+2 \\ & =2 \\ & \end{aligned}\thereforeDimensionalformulaofenergyDimensional formula of energy=F A T^2
Practice Units and Dimensions on Quantrex Academy →

More from Units and Dimensions

If the errors involved in the measurement of a side and the mass of a cube are 2\% and… MHT CET Medical 2026If the mass of the object is measured as m = (7 ∓ 0.14) kg and the density is measured as… MHT CET Medical 2026Consider that σ_s , k_B , b represent Stefan-Boltzmann constant, Boltzmann constant and… NEET 2026The speed of light in vacuum is taken as unity. If light takes 6 min 40 s to reach the… NEET 2026Each side of a metallic cube of mass 5.580 kg is measured to be 9.0 cm. Keeping the… NEET 2026A physical quantity P is related to four observations a, b, c and d as follows : P=a^3… NEET 2025A balloon is made of a material of surface tension S and its inflation outlet (from where… NEET 2025The quantities which have the same dimensions as those of solid angle are: NEET 2024 Full Units and Dimensions list All NEET PYQs