Question

A force defined by F = αt² + βt acts on a particle at a given time t. The factor which is dimensionless, if α and β are constants, is ______.

Options

• αβt

• αβ/t

• βt/α

• αt/β

Answer 1

A force defined by F = αt² + βt acts on a particle at a given time t. The factor which is dimensionless, if α and β are constants, is αt/β.

Explanation:

Given: F = αt² + βt

The dimensions of force are:

F = [M L T⁻²]

From αt²:

αt² = [M L T⁻²]

⇒ α = `([M L T^-2])/T^2

= M L T⁻⁴

From βt:

βt = M L T⁻²

⇒ β = `([M L T^-2])/T`

= M L T⁻³

`alpha/beta = ([M L T^-4])/([M L T^-3])`

= T⁻¹

αt = M L T⁻⁴ . T = M L T⁻³

β = M L T⁻³

So,

`(alpha t)/beta` = 1