Question

check the correctness of the v=u+at useing dimensional method

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

Answer 2

Given equation :-

v = u + at

$\rule{150}{2}$

We know,

• dimensional formula of v = (M⁰LT⁻¹)

• dimensional formula of u = (M⁰LT⁻¹)

• dimensional formula of a = (M⁰LT⁻²)

• dimensional formula of t = (M⁰L⁰T)

$\rule{150}{2}$

→ LHS  is the dimensional formula of v = (M⁰LT⁻¹)

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

= (M⁰LT⁻¹) + (M⁰LT⁻²) × (M⁰L⁰T)

= (M⁰LT⁻¹) + (M⁰LT⁻¹)

= 2(M⁰LT⁻¹)

$\rule{150}{2}$

2 is a dimensionless constant, so LHS = RHS

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