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If linear momentum is increased by 50%, the kinetic energy will increase by
- a)50%
- b)125%
- c)225%
- d)25%
Correct answer is option 'B'. Can you explain this answer?
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If linear momentum is increased by 50%, the kinetic energy will incre...
If linear momentum is increased by 50%, the kinetic energy will increase by 125%
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If linear momentum is increased by 50%, the kinetic energy will incre...
Explanation:
Increasing linear momentum by 50% means the new linear momentum is 1.5 times the original linear momentum.
Kinetic Energy Formula:
The kinetic energy (KE) of an object is given by the formula KE = 0.5 * m * v^2, where m is the mass of the object and v is its velocity.
Relationship between Linear Momentum and Kinetic Energy:
The linear momentum (p) of an object is given by the formula p = m * v, where m is the mass of the object and v is its velocity. Linear momentum is directly proportional to velocity.
Effect of Increasing Linear Momentum on Kinetic Energy:
When linear momentum is increased by 50%, the velocity of the object also increases. Since kinetic energy is directly proportional to the square of velocity, the kinetic energy will increase by a greater percentage than the increase in linear momentum.
Calculation:
- Let's assume the initial linear momentum is p and initial kinetic energy is KE.
- After increasing linear momentum by 50%, the new linear momentum is 1.5p.
- Since linear momentum is directly proportional to velocity, the new velocity is also 1.5 times the initial velocity.
- Substituting the new velocity into the kinetic energy formula, the new kinetic energy is 1.5^2 times the initial kinetic energy.
- Therefore, the kinetic energy will increase by 1.5^2 = 2.25 times, which is equal to a 125% increase.
Therefore, the correct answer is option 'B' - 125%.
Increasing linear momentum by 50% means the new linear momentum is 1.5 times the original linear momentum.
Kinetic Energy Formula:
The kinetic energy (KE) of an object is given by the formula KE = 0.5 * m * v^2, where m is the mass of the object and v is its velocity.
Relationship between Linear Momentum and Kinetic Energy:
The linear momentum (p) of an object is given by the formula p = m * v, where m is the mass of the object and v is its velocity. Linear momentum is directly proportional to velocity.
Effect of Increasing Linear Momentum on Kinetic Energy:
When linear momentum is increased by 50%, the velocity of the object also increases. Since kinetic energy is directly proportional to the square of velocity, the kinetic energy will increase by a greater percentage than the increase in linear momentum.
Calculation:
- Let's assume the initial linear momentum is p and initial kinetic energy is KE.
- After increasing linear momentum by 50%, the new linear momentum is 1.5p.
- Since linear momentum is directly proportional to velocity, the new velocity is also 1.5 times the initial velocity.
- Substituting the new velocity into the kinetic energy formula, the new kinetic energy is 1.5^2 times the initial kinetic energy.
- Therefore, the kinetic energy will increase by 1.5^2 = 2.25 times, which is equal to a 125% increase.
Therefore, the correct answer is option 'B' - 125%.
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If linear momentum is increased by 50%, the kinetic energy will increase bya)50%b)125%c)225%d)25%Correct answer is option 'B'. Can you explain this answer?
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