Correct option is (1) 1 : 9
Given,
Mass of 2 bodies = m
Velocity of body 1 (v1) = v
The velocity of body 2 (v2) = 3v
Kinetic Energy(K.E) = \(\frac{1}{2}\)mv2, where m is mass and v is velocity.
Finding the ratio of kinetic energies of 2 bodies
The kinetic energy of body 1, KE1 = 12 mv2.
The kinetic energy of body 2,
\(KE_2 = \frac {1}{2} m (3v)^2\)
\(\frac {KE_1}{KE_2} = \frac {\frac {1}{2}mv^2}{\frac{1}{2}m(9v^2)}\)
\(\frac {KE_1}{KE _2} = \frac {1}{9}\)
Hence, the ratio of the kinetic energies is given by KE1 : KE2 = 1 : 9.
