Kinetic Energy and Mass Speed Relation – Rankers Physics

Kinetic Energy and Momentum: Practice Problem & Solution

Arun has \(\left(\frac{1}{3}\right)^{\text{rd}}\) of the kinetic energy as that of Raunak when they both run. If Raunak has half the mass of Arun, then the relationship between the speed of Arun \(v'\) and speed of Raunak \(v\) is
\(v' = \frac{v}{\sqrt{6}}\)
\(v' = \frac{v}{\sqrt{3}}\)
\(v' = \frac{v}{\sqrt{2}}\)
\(v' = v\)

Solution Explained:

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:

Let \(m_A = 2m_R\). Given \(K_A = \frac{1}{3}K_R ⇒ \frac{1}{2}m_A v'^2 = \frac{1}{3}\left(\frac{1}{2}m_R v^2\right)\). Substituting \(m_A = 2m_R\), we get \(2v'^2 = \frac{1}{3}v^2 ⇒ v' = \frac{v}{\sqrt{6}}\).

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Your email address will not be published.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. Assertion (A): If in a round trip work done by a force is zero then force is conservative. Reason (R): Work done by conservative force field is independent of path.  
2. Assertion (A): An athlete accelerates from rest to its maximum speed due to friction between his shoes and track. Reason (R): Positive work done by frictional force increases the kinetic energy of athlete.
3. Assertion (A): Work done is positive when force acts in the direction of displacement. Reason (R): Work done by frictional force can not be positive.
4. A particle of mass $m$ is driven by a machine that delivers a constant power $k$ watts. If the particle starts from rest the force on the particle at time $t$ is: (2015)
5. When a long spring is stretched by \(2\text{ cm}\), its potential energy is \(U\). If the spring is stretched by \(10\text{ cm}\), the potential energy stored in it will be: (2003)