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

Step-by-step solution

Let energy E=F^x A^y T^3 Writing the dimensions on both sides aligned & [ ML ^2 ~T ⁻² ]= [ MLT ⁻² ]^x [ LT ⁻² ]^y[ ~T ]^2 & [ ML ^2 ~T ⁻² ]= [ M ^x ~L ^ x+y ~T ^ -2 x-2 y+z ] aligned On comparing both sides aligned & x=1 & x+y=2 & y=2-x=2-1=1 & and -2 x-2 y+z=-2 & -2 1-2 1+z=-2 & z=-2+2+2 & =2 & aligned Dimensional formula of energy =F A T^2