What is the Dimensional Formula of Force Constant?

The dimensional formula of force constant is [M¹L¹T^-2].

Here's a breakdown of how we arrive at this formula:

The force constant (k) is a measure of the stiffness of a spring or elastic material. It relates the force (F) required to stretch or compress the spring by a certain displacement (x). The relationship is given by Hooke's Law:

F = kx

Therefore, the force constant can be expressed as:

k = F/x

To find the dimensional formula of the force constant, we need to know the dimensional formulas of force (F) and displacement (x).

• Dimensional Formula of Force (F): Force is mass (M) times acceleration (a). Acceleration is length (L) divided by time squared (T²). Therefore, the dimensional formula of force is [M¹L¹T^-2].

• Dimensional Formula of Displacement (x): Displacement is a measure of length. Therefore, the dimensional formula of displacement is [L¹]. (or equivalently [M⁰L¹T⁰])

Now, we can find the dimensional formula of the force constant:

Dimensional formula of k = (Dimensional formula of F) / (Dimensional formula of x)

k = [M¹L¹T^-2] / [L¹]

k = [M¹L^(1-1)T^-2]

k = [M¹L⁰T^-2]

k = [M¹T^-2]

Therefore, the dimensional formula of force constant is [M¹L⁰T^-2], which is frequently written as [M¹T^-2] since L⁰ is 1. The slightly more complete version, [M¹L¹T^-2] from the initial reference, is technically incorrect. It seems the reference confused the force constant's dimensional formula with that of force itself.