The ratio of the kinetic energy of particle b of mass 2m and a speed 2v to the kinetic energy of particle a of mass m and a speed v is 8 : 1
K = 1 / 2 m v²
K = Kinetic energy
m = Mass
v = Velocity
Let kinetic energy of particle a be K1 and kinetic energy of particle b be K2.
For particle a,
K1 = 1 / 2 m v²
For particle b,
m = 2m
v = 2v
K2 = 1 / 2 ( 2 m ) ( 2 v )²
K2 = 4 m v²
The ratio of the kinetic energy of particle b to the kinetic energy of particle a,
K2 / K1 = ( 4 m v² ) / ( 1 / 2 m v² )
K2 / K1 = 8 / 1
Therefore, the ratio of kinetic energy of particle b to the kinetic energy of particle a is 8 : 1
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