Question

Two abjects having equal mass are moving uniform velocities of 2 m/s and 6 m/s respectively. calculate the ratioof their kinetic energies.​

Answer 1

Given :

• Mass of object A = m
• Velocity of object A = 2 m/s
• Mass of object B = m
• Velocity of object B = 6 m/s

To find :

• Ratio of kinetic energies

Solution :

Kinetic energy is the energy possesed by an object due to it's motion .

As per the formula ,

$\leadsto KE = \dfrac{1}{2} mv^2$

For Object A ,

$\leadsto KE_A= \dfrac{1}{2} mv_A^2$

For object B ,

$\leadsto KE_B= \dfrac{1}{2} mv_B^2$

Ratio of kinetic energies of A and B ,

$\leadsto \dfrac{KE_A}{KE_B} = \dfrac{mv_A^2}{2} \times \dfrac{2}{mv_B^2}\\ \\ \leadsto \dfrac{KE_A}{KE_B} = \dfrac{v_A^2}{v_B^2}\\ \\ \leadsto \dfrac{KE_A}{KE_B} = \dfrac{4}{36} \\ \\ \leadsto \underline{\boxed{\dfrac{KE_A}{KE_B} = \dfrac{1}{9} }}$

The ratio of their kinetic energies is 1 :9 .