Question

The displacement x of a particle at time t along a straight line is given by
X=α-βt+ϒt^2.
find the dimensions of α, β and ϒ

Answer 1

Answer:-

α= [L T^-1 ]

β = [ L T^-2 ]

ϒ = [ L T^-3 ]

Given:-

Displacement x of a particle is given by:-

X = α-βt+ϒt^2.

To find :-

Dimensions of α,β and ϒ.

Solution:-

The dimensional formula of displacement is [ L T ^-1]

by using principal of homeginity ,

[ LT^-1] = α - β[ T ] + ϒ[ T ]^2.

Now,

[L T^-1 ] = α

[ L T^-1 ] = β[ T ]

β = [ L T^-2 ]

[ L T^-1 ] = ϒ[ T^2]

ϒ = [ L T^-3 ]