Given information
The kinetic energy of one fragment is double that of the other.
The explosion splits the object into 
fragments.
Step-by-step explanation
We can say that,
the two fragments' masses = 
momenta = 
kinetic energies = 
The initial momentum of the object = 
,Because the object is stationary before it explodes
After explosion,
At first we have to know the definition of momentum. So, Momentum is a measure of mass in motion: how much mass is moving and how fast. It is commonly denoted by the letter p.
The last momentum of the system = 
.
The explosion follows the law of momentum conservation because it explodes without any external force acting on the object.
Therefore,
So,
The kinetic energy of each fragment is associated with momentum and mass by the following equation.
and 
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Physics: Principles with Applications
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