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.

Asked by rajneesh kumar | 5th Dec, 2013, 08:38: PM

Expert Answer:

Let, 
 
Mass of ball a = Ma   
Mass of ball b = Mb
Velosity of ball a = Va
Velosity of ball b = Vb
 
Given that,
 
Ma = 2 Mb      
Va = Vb/2
 
Kinetic energy of ball a   Ka = 1/2 x  Ma  x Va2
 
Kinetic energy of ball b   Kb = 1/2 x  Mb  x Vb2
 
Ka = 1/2 x  Ma  x Va2
    =1/2 x (2 Mb) x (Vb/2)2
    = Mb x 1/4 x Vb2
    = 1/2 (1/2 x  Mb  x Vb2)
    = 1/2 Kb
 
Ka /Kb = 1/2
 
Hence the ratio of kinetic energies of ball a and ball b is = 1/2

Answered by Komal Parmar | 6th Dec, 2013, 12:33: AM

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