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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
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