Question:
A bomb of mass 16 kg at rest explodes into two pieces of masses 4 kg and 12 kg. The velocity of the 12 kg mass is 4 $ms^{-1}.$The kinetic energy of the other mass is:
A bomb of mass 16 kg at rest explodes into two pieces of masses 4 kg and 12 kg. The velocity of the 12 kg mass is 4 $ms^{-1}.$The kinetic energy of the other mass is:
Updated On: Mar 10, 2024
- 144J
- 288J
- 192J
- 96J
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The Correct Option is B
Solution and Explanation
Here momentum of the system is remaining conserved as no external force is acting on the bomb (system). Initial momentum (before explosion) = Final momentum (after explosion) Let velocity of 4 kg mass is v m/s. From momentum conservation we can say that its direction is opposite to velocity of 12 kg mass.
$from \, \quad\vec{P}_{i}=\vec{P}_{f}$
$\Rightarrow 0=12\times4-4\times v \Rightarrow v=12 m/ s$
KE of 4 kg mass =$\frac{4\times\left(12\right)^{2}}{2} =288 J $
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Concepts Used:
Momentum
It can be defined as "mass in motion." All objects have mass; so if an object is moving, then it is called as momentum.
the momentum of an object is the product of mass of the object and the velocity of the object.
Momentum = mass • velocity
The above equation can be rewritten as
p = m • v
where m is the mass and v is the velocity.
Momentum is a vector quantity and the direction of the of the vector is the same as the direction that an object.