Question

The distance covered by a particle in time t is given by x = a + bt + ct² + dt³;find the dimensions of a, b, c and d.
Concept of Physics - 1 , HC VERMA , Chapter "Introduction to Physics".

Answer 1

$<b><font face=Copper black size=4 colour=purple>$
$<b><marquee direction = "up" > <h3>$Applying The Principle of Homogeneity -

Given -

x = a + bt + ct² + dt³

Here, x = Distance

Dimensions of distance = [ L ]

Now,

x = a

a = [ L ]

✒ a = $\mathsf{[ \ M^0L^1T^0 \ ]}$

x = bt

b = x / t

b = [ L ] / [ T ]

✒ b = $\mathsf{[ \ M^0L^1{T}^{-1} \ ]}$

x = ct²

c = x / t²

c = [ L ] / [ T² ]

✒ c = $\mathsf{[ \ M^0L^1{T}^{-2} \ ]}$

x = dt³

d = x / t³

d = [ L ] / [ T³ ]

✒ d = $\mathsf{[ \ M^0L^1{T}^{-3} \ ]}$

^^"