Maharashtra State PSC Model Paper 1

CONCEPT:

• The dimensional formula is used to express any physical quantity in terms of fundamental quantities.
• Fundamental quantity: 
  • A quantity that can be measured is called a physical quantity. 
  • Fundamental quantities are those which cannot be expressed or measured in terms of other physical quantities. 
  • The SI system has seven fundamental quantities i.e. time, length, mass, electric current, thermodynamic temperature, amount of substance, and luminous intensity. 
  • The dimensional formula of a fundamental quantity will only have the fundamental quantities.
  • The seven fundamental quantities along with their dimensions are as follows

EXPLANATION:

• Distance is a measure of length and hence it's dimensional formula is [L].

In the given expression: 

⇒ s = A + Bt + Ct2, the terms A, Bt, and Ct² are added, and hence all of them will have the dimensional formula of distance.

• A is independent of any other variables and thus its dimensional formula is [L].
• In the term Bt, t represents time and has the dimensional formula [T]. Thus, $\mathrm{B}\left[\mathrm{T}\right]=\left[\mathrm{L}\right]\Rightarrow \mathrm{B}=\left[{\mathrm{LT}}^{-1}\right]$
• In the term ${\mathrm{Ct}}^2,$ t represents time and has the dimensional formula $\left[{\mathit{T}}^2\right]$. Thus, $\mathrm{C}\left[{\mathrm{T}}^2\right]=\left[\mathrm{L}\right]\Rightarrow \mathrm{C}=\left[{\mathrm{LT}}^{-2}\right]$