Dimensional Formula of Force Constant

The dimensional formula of force constant is given by,

[M¹ L⁰ T^-2]

Where,

• M = Mass
• L = Length
• T = Time

Derivation

Force Constant= Force × [Displacement]^-1 . . . (1)

Since, Force = m × a

Therefore, the dimensions of force = [M¹ L¹ T^-2] . . . (2)

And, the dimensional formula of displacement = [M⁰ L¹ T⁰] . . . . (3)

On substituting equation (2) and (3) in equation (1) we get,

Force Constant= Force × [Displacement]^-1

= [M¹ L¹ T^-2] × [M⁰ L¹ T⁰]^-1 = [M¹ L⁰ T^-2].

Therefore, the force constant is dimensionally represented as [M¹ L⁰ T^-2].

⇒ Check Other Dimensional Formulas:

• Dimensions of Universal Gas Constant
• Dimensions of Impedance
• Dimensions of Rotational Kinetic Energy
• Dimensions of Gravitational Potential Energy
• Dimensions of Potential Energy

Internal and External Forces