Kinetic Energy and Momentum Dimensions – Rankers Physics

Kinetic Energy and Momentum: Practice Problem & Solution

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

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Kinetic Energy and Momentum. Understanding the underlying formula is key to arriving at the correct answer below:

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.

Leave a Reply

Your email address will not be published. Required fields are marked *

Similar Practice Questions

Explore conceptually related problems to test your knowledge.

1. A force \( \vec{F} = (3x\hat{i} + 4\hat{j})\text{ Newton} \) (where \( x \) is in metres) acts on a particle which moves from a position \( (2\text{ m}, 3\text{ m}) \) to \( (3\text{ m}, 0\text{ m}) \). Then the work done is:
2. The graph between √E and 1/p is (E = kinetic energy and p = momentum):
3. Assertion (A): Power delivered by all forces acting on a particle moving in a uniform circular motion is always zero. Reason (R): Work done by all forces acting on a particle moving in a uniform circular motion is zero as KE remains constant.  
4. A car of mass $m$ starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude $P_0$. The instantaneous velocity of this car is proportional to: (2012 Mains)
5. Two bodies of masses \(m\) and \(4m\) are moving with equal kinetic energies. The ratio of their linear momenta is: (1998, 97, 89)