Kinetic Energy and Momentum Dimensions – Rankers Physics
Topic: Work Energy and Power
Subtopic: Kinetic Energy and Momentum

Kinetic Energy and Momentum Dimensions

Assertion (A): A body cannot have kinetic energy without having linear momentum but it can have momentum without having mechanical energy.
Reason (R): Linear momentum and energy have same dimensions.
 
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution:

Assertion (A) is false:

If a body has linear momentum (\(p \neq 0\)), it must have velocity (\(v \neq 0\)), which implies it must also have kinetic energy (\(KE = \frac{1}{2}mv^2 \neq 0\)). Since kinetic energy is a component of mechanical energy, it cannot have momentum without mechanical energy.

Reason (R) is false: Linear momentum has dimensions \(MLT^{-1}\) while energy has dimensions \(ML^2T^{-2}\), which are different.

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