Question

check correctness of formula v =u+at. By dimensional method

Answer 1

dimensional formula

v=[M^0L¹T^-¹]

u=[ M^0L^¹T^-¹ ]

a=[M^0L¹T^-² ]

t=[T ]

we have v =u+at

[M^0L¹T^-¹]=[M^0L¹T^-¹]+[M^0L¹T^-² ][T]

[M^0L¹T^-¹]=[M^0L¹T^-¹]+[M^0L¹T^-¹]

LHS =RHS

hence given formula is dimensionally correct

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.