Question

using dimentional analysis check the correctness of the given physical equation v= u + at​

Answer 1

Answer:

L.H.S=v=[LT^-1]

R.H.S=u+at=[LT^-1]+[LT^-2].[T]

=[LT^-1][LT^-1]=2[LT^-1]=[LT^-1]

so L.H.S=R.H.S

Explanation:

remember that constant has no dimensions

Answer 2

Given equation :-

v = u + at

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.