Question

Two bodies having equal masses are moving with uniform speeds of v and 2v respectively. Find the ratio of their kinetic energies.

Answer 1

Let the masses of the two bodies be (m₁) = m kg and (m₂) = m kg .
Velocity of the first body, (v₁) = v m/s
Velocity of the first body, (v₂) = 2v m/s
The required ratio is-
= `"(Kinetic energy)"_1/"(Kinetic energy)"_2`
= `(1/2 (m_1)(v_1)^2)/(1/2 (m_2)(v_2)^2)`
So put the values to get , 
= `(1)^2/(2)^2`
= `1/4`

The ratio of K.E is, K.E of body 1 : K.E of body 2 = 1 : 4.