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The momentum of a bullet of mass 20 g fired from a gun is 10 kg. m/s. The kinetic energy of this bulletin kJ will be
- a)5
- b)1.5
- c)2.5
- d)25
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The momentum of a bullet of mass 20 g fired from a gun is 10 kg. m/s....
K.E. = ½ mv2 = p2/2m (m = 20 g = 0.02kg)
= 10×10/2×0.02 = 2500 j = 2.5 kj
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The momentum of a bullet of mass 20 g fired from a gun is 10 kg. m/s....
Understanding Momentum and Kinetic Energy
To solve for the kinetic energy of the bullet, we first need to understand the relationship between momentum and kinetic energy.
Definitions
- Momentum (p): It is defined as the product of mass (m) and velocity (v) of an object.
- Formula: p = m * v
- Kinetic Energy (KE): It is defined as the energy that an object possesses due to its motion.
- Formula: KE = (1/2) * m * v^2
Given Information
- Mass of the bullet (m): 20 g = 0.020 kg (conversion to kg)
- Momentum (p): 10 kg·m/s
Finding Velocity
Using the momentum formula:
- p = m * v
- Rearranging gives us: v = p / m
- Substituting the values:
- v = 10 kg·m/s / 0.020 kg = 500 m/s
Calculating Kinetic Energy
Now that we have the velocity, we can find the kinetic energy:
- KE = (1/2) * m * v^2
- KE = (1/2) * 0.020 kg * (500 m/s)^2
- KE = 0.010 kg * 250000 m²/s²
- KE = 2500 J
Converting to kJ
Since 1 kJ = 1000 J:
- KE = 2500 J = 2.5 kJ
Conclusion
The kinetic energy of the bullet is 2.5 kJ, thus confirming that option 'C' is correct.
To solve for the kinetic energy of the bullet, we first need to understand the relationship between momentum and kinetic energy.
Definitions
- Momentum (p): It is defined as the product of mass (m) and velocity (v) of an object.
- Formula: p = m * v
- Kinetic Energy (KE): It is defined as the energy that an object possesses due to its motion.
- Formula: KE = (1/2) * m * v^2
Given Information
- Mass of the bullet (m): 20 g = 0.020 kg (conversion to kg)
- Momentum (p): 10 kg·m/s
Finding Velocity
Using the momentum formula:
- p = m * v
- Rearranging gives us: v = p / m
- Substituting the values:
- v = 10 kg·m/s / 0.020 kg = 500 m/s
Calculating Kinetic Energy
Now that we have the velocity, we can find the kinetic energy:
- KE = (1/2) * m * v^2
- KE = (1/2) * 0.020 kg * (500 m/s)^2
- KE = 0.010 kg * 250000 m²/s²
- KE = 2500 J
Converting to kJ
Since 1 kJ = 1000 J:
- KE = 2500 J = 2.5 kJ
Conclusion
The kinetic energy of the bullet is 2.5 kJ, thus confirming that option 'C' is correct.
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The momentum of a bullet of mass 20 g fired from a gun is 10 kg. m/s. The kinetic energy of this bulletin kJ will bea)5b)1.5c)2.5d)25Correct answer is option 'C'. Can you explain this answer?
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