Kinetic Energy and Mass Speed Relation – Rankers Physics
Topic: Work Energy and Power
Subtopic: Kinetic Energy and Momentum

Kinetic Energy and Mass Speed Relation

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:

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Your email address will not be published.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 *