Question

Using the method of dimension analysis show which of the following equation are correct......V=u +at,V=U+St,V raise to power 2=U raise to power 2+2 as ,V=U+2as?

Answer 1

Equation is v=u+at

dimensional formula of v=(M°LT^-1)

dimensional formula of u=(M°LT^-1)

dimensional formula of a=(M°LT^-2)

dimensional formula of t=(M°L°T)

LHS is the dimensional formula of v=(M°LT^-1)

RHS=dimensional formula of u+dimensional formula of a×dimensional formula of t

=(M°LT^-1)+(M°LT^-2)×(M°L°T)

=(M°LT^-1)+(M°LT^-1)

=2(M°LT^-1)

2 is a dimensionless constant ,therefore LHS=RHS

Hence,the given relationship(equation)is dimensionally correct.