Question

Dimension of force is :
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Answer 1

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Dimensional Formula of Force

The dimensional formula of force is given by,

$\boxed{\sf{ {m}^{1} {l}^{1} {t}^{ - 2} }}$

Where,

• M = Mass
• L = Length
• T = Time

Derivation

Force = Mass × Acceleration . . . . (1)

Since, acceleration =

$velocity × [time]^{–1} = [LT^{-1}] × [T]^{-1}$

Therefore, the dimensional formula of acceleration = [LT^-2] . . . . (2)

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

Force = m × a

Or,

$F = [M] × [L^{1 }T^{-2}] = M^{1} L^{1 }T^{-2}.$

Therefore, Force is dimensionally represented as

$M{^1 }L^{1} T^{-2}.$