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The kinetic energy of a body becomes 4 times its initial value. The new linear momentum will be
- a)Same as initial value
- b)Four times the initial value
- c)Twice the initial value
- d)Eight times the initial value
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The kinetic energy of a body becomes 4 times its initial value. The ne...
KE = P2/2m
When KE becomes 4 times, p2 is 4 times or p becomes 2 times
When KE becomes 4 times, p2 is 4 times or p becomes 2 times
Most Upvoted Answer
The kinetic energy of a body becomes 4 times its initial value. The ne...
Kinetic Energy and Linear Momentum
Kinetic energy and linear momentum are two important concepts in physics that describe the motion of an object. Understanding the relationship between these two quantities is crucial in analyzing the behavior of moving objects.
Kinetic Energy (KE)
Kinetic energy is the energy possessed by an object due to its motion. It is given by the equation:
KE = (1/2) mv^2
where KE is the kinetic energy, m is the mass of the object, and v is its velocity. The kinetic energy is directly proportional to both the mass and the square of the velocity of the object.
Linear Momentum (p)
Linear momentum is the product of an object's mass and its velocity. It is given by the equation:
p = mv
where p is the linear momentum, m is the mass of the object, and v is its velocity. The linear momentum is directly proportional to both the mass and the velocity of the object.
Relationship between Kinetic Energy and Linear Momentum
The relationship between kinetic energy and linear momentum can be derived by squaring the equation for linear momentum:
p^2 = (mv)^2 = m^2v^2
Since kinetic energy is defined as (1/2) mv^2, we can rewrite the equation for linear momentum as:
p^2 = 2m(KE)
Therefore, the linear momentum is equal to the square root of twice the kinetic energy:
p = sqrt(2m(KE))
Effect of Increasing Kinetic Energy on Linear Momentum
Given the equation for linear momentum, if the kinetic energy of an object increases, the linear momentum will also increase. In the given question, the kinetic energy of the body becomes 4 times its initial value. Let's analyze the effect on linear momentum:
Initial kinetic energy = KE_initial
Final kinetic energy = 4(KE_initial)
Using the equation for linear momentum, we can compare the initial and final linear momenta:
p_initial = sqrt(2m(KE_initial))
p_final = sqrt(2m(4(KE_initial)))
Simplifying the equation for final linear momentum, we get:
p_final = sqrt(8m(KE_initial))
Since the initial linear momentum is given by p_initial = sqrt(2m(KE_initial)), we can see that:
p_final = sqrt(4(2m(KE_initial)))
= 2(sqrt(2m(KE_initial)))
= 2p_initial
Therefore, the new linear momentum will be twice the initial value when the kinetic energy becomes 4 times its initial value. Hence, option 'c' is the correct answer.
Kinetic energy and linear momentum are two important concepts in physics that describe the motion of an object. Understanding the relationship between these two quantities is crucial in analyzing the behavior of moving objects.
Kinetic Energy (KE)
Kinetic energy is the energy possessed by an object due to its motion. It is given by the equation:
KE = (1/2) mv^2
where KE is the kinetic energy, m is the mass of the object, and v is its velocity. The kinetic energy is directly proportional to both the mass and the square of the velocity of the object.
Linear Momentum (p)
Linear momentum is the product of an object's mass and its velocity. It is given by the equation:
p = mv
where p is the linear momentum, m is the mass of the object, and v is its velocity. The linear momentum is directly proportional to both the mass and the velocity of the object.
Relationship between Kinetic Energy and Linear Momentum
The relationship between kinetic energy and linear momentum can be derived by squaring the equation for linear momentum:
p^2 = (mv)^2 = m^2v^2
Since kinetic energy is defined as (1/2) mv^2, we can rewrite the equation for linear momentum as:
p^2 = 2m(KE)
Therefore, the linear momentum is equal to the square root of twice the kinetic energy:
p = sqrt(2m(KE))
Effect of Increasing Kinetic Energy on Linear Momentum
Given the equation for linear momentum, if the kinetic energy of an object increases, the linear momentum will also increase. In the given question, the kinetic energy of the body becomes 4 times its initial value. Let's analyze the effect on linear momentum:
Initial kinetic energy = KE_initial
Final kinetic energy = 4(KE_initial)
Using the equation for linear momentum, we can compare the initial and final linear momenta:
p_initial = sqrt(2m(KE_initial))
p_final = sqrt(2m(4(KE_initial)))
Simplifying the equation for final linear momentum, we get:
p_final = sqrt(8m(KE_initial))
Since the initial linear momentum is given by p_initial = sqrt(2m(KE_initial)), we can see that:
p_final = sqrt(4(2m(KE_initial)))
= 2(sqrt(2m(KE_initial)))
= 2p_initial
Therefore, the new linear momentum will be twice the initial value when the kinetic energy becomes 4 times its initial value. Hence, option 'c' is the correct answer.
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The kinetic energy of a body becomes 4 times its initial value. The new linear momentum will bea)Same as initial valueb)Four times the initial valuec)Twice the initial valued)Eight times the initial valueCorrect answer is option 'C'. Can you explain this answer?
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The kinetic energy of a body becomes 4 times its initial value. The new linear momentum will bea)Same as initial valueb)Four times the initial valuec)Twice the initial valued)Eight times the initial valueCorrect answer is option 'C'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The kinetic energy of a body becomes 4 times its initial value. The new linear momentum will bea)Same as initial valueb)Four times the initial valuec)Twice the initial valued)Eight times the initial valueCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The kinetic energy of a body becomes 4 times its initial value. The new linear momentum will bea)Same as initial valueb)Four times the initial valuec)Twice the initial valued)Eight times the initial valueCorrect answer is option 'C'. Can you explain this answer?.
The kinetic energy of a body becomes 4 times its initial value. The new linear momentum will bea)Same as initial valueb)Four times the initial valuec)Twice the initial valued)Eight times the initial valueCorrect answer is option 'C'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The kinetic energy of a body becomes 4 times its initial value. The new linear momentum will bea)Same as initial valueb)Four times the initial valuec)Twice the initial valued)Eight times the initial valueCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The kinetic energy of a body becomes 4 times its initial value. The new linear momentum will bea)Same as initial valueb)Four times the initial valuec)Twice the initial valued)Eight times the initial valueCorrect answer is option 'C'. Can you explain this answer?.
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