Question

Two bodies A and B of masses 1kg and 4kg respectively have equal momenta find ratio of their K. E solve this numerical​

Answer 1

Given :

▪ Mass of body A = 1kg

▪ Mass of body B = 4kg

▪ A and B have equal momenta.

To Find :

▪ Ratio of their kinetic energies.

Concept :

→ The kinetic energy of the particle is given by

$\star\sf\:K=\dfrac{1}{2}mv^2$

→ As momentum, p = mv

$\therefore\bf\:K=\dfrac{1}{2}m{\huge{(}}\dfrac{p^2}{m^2}{\huge{)}}=\dfrac{P^2}{2m}$

Calculation :

$\rightarrow\sf\:P_A=P_B\\ \\ \rightarrow\sf\:\sqrt{2m_AK_A}=\sqrt{2m_BK_B}\\ \\ \rightarrow\sf\:\dfrac{K_A}{K_B}=\dfrac{m_B}{m_A}=\dfrac{4}{1}\\ \\ \dashrightarrow\underline{\boxed{\bf{\gray{K_A:K_B=4:1}}}}\:\green{\bigstar}$