The mass of a ball a is double the mass of another ball b.The ball a moves at half the speed of the ball b.Calculate the ratio of the kinetic energy of a to the kinetic energy b.

Let, 

 

Mass of ball a = M_a   

Mass of ball b = M_b

Velosity of ball a = V_a

Velosity of ball b = V_b

 

Given that,

 

M_a = 2 M_b      

V_a = V_b/2

 

Kinetic energy of ball a   K_a = 1/2 x  M_a  x V_a²

 

Kinetic energy of ball b   K_b = 1/2 x  M_b  x V_b²

 

K_a = 1/2 x  M_a  x V_a²

    =1/2 x (2 M_b) x (V_b/2)²

    = M_b x 1/4 x V_b²

    = 1/2 (1/2 x  M_b  x V_b²)

    = 1/2 K_b

 

K_a /K_b = 1/2

 

Hence the ratio of kinetic energies of ball a and ball b is = 1/2