A body of mass `m_1 = m` moving with a velocity `v_1 = v` in the x-direction collides with another body of the same mass `m_2 = m` moving in the y-direction with the same speed `v_2 = v`. Then coalesce into one body during the collision.
The fraction of initial kinetic energy transformed into heat during the collision is

Options

A. `1/2`
B. `1/4`
C. `2/3`
D. `1/3`

Answer

A

Explanation

Initial kinetic energy
`K_1 = 1/2 m_1v_1^2 + 1/2 m_2v_2^2 = mv^2`
From eqn. (3), we have `v. = v//sqrt(2)`. Final kinetic energy is
`k_f = 1/2 (m_1 + m_2)(v.)^2 = 1/2 xx 2m xx (v^2)/2 = 1/2 m v^2`