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The linear momentum of a particle varies with time t as p = a + bt + ct2. Which of the following statement is correct?
- a)force varies with time in a quadratic manner
- b)Force is time-dependent
- c)The velocity of the particle is proportional to time
- d)The displacement of the particle is proportional to t.
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The linear momentum of a particle varies with time t as p = a + bt + c...
Clearly, the force is time-dependent.
Most Upvoted Answer
The linear momentum of a particle varies with time t as p = a + bt + c...
Linear Momentum and its Relation to Force, Velocity, and Displacement:
The linear momentum (p) of a particle is defined as the product of its mass (m) and velocity (v), given by the equation p = mv. In this question, the linear momentum of a particle is given as p = a bt ct^2, where a, b, and c are constants.
Relation between Force and Linear Momentum:
According to Newton's second law of motion, force (F) is defined as the rate of change of momentum with respect to time. Mathematically, it can be expressed as F = dp/dt, where dp represents the change in momentum and dt represents the change in time. Therefore, the force acting on a particle is given by the derivative of its momentum with respect to time.
Understanding the given expression for Linear Momentum:
The expression p = a bt ct^2 represents a polynomial function of time. Differentiating this expression with respect to time will give us the rate of change of momentum, which corresponds to the force acting on the particle.
Derivative of the given expression:
Taking the derivative of p = a bt ct^2 with respect to time yields:
dp/dt = a b + 2a c t
Thus, the force acting on the particle, F = dp/dt, is indeed time-dependent as it contains a term involving time (t).
Conclusion:
From the above derivation, it is evident that the force acting on the particle is time-dependent. Therefore, the correct statement is option B: Force is time-dependent.
It is important to note that the other options are not correct based on the given information. The expression for linear momentum does not directly provide information about the dependence of force on time, velocity on time, or displacement on time.
The linear momentum (p) of a particle is defined as the product of its mass (m) and velocity (v), given by the equation p = mv. In this question, the linear momentum of a particle is given as p = a bt ct^2, where a, b, and c are constants.
Relation between Force and Linear Momentum:
According to Newton's second law of motion, force (F) is defined as the rate of change of momentum with respect to time. Mathematically, it can be expressed as F = dp/dt, where dp represents the change in momentum and dt represents the change in time. Therefore, the force acting on a particle is given by the derivative of its momentum with respect to time.
Understanding the given expression for Linear Momentum:
The expression p = a bt ct^2 represents a polynomial function of time. Differentiating this expression with respect to time will give us the rate of change of momentum, which corresponds to the force acting on the particle.
Derivative of the given expression:
Taking the derivative of p = a bt ct^2 with respect to time yields:
dp/dt = a b + 2a c t
Thus, the force acting on the particle, F = dp/dt, is indeed time-dependent as it contains a term involving time (t).
Conclusion:
From the above derivation, it is evident that the force acting on the particle is time-dependent. Therefore, the correct statement is option B: Force is time-dependent.
It is important to note that the other options are not correct based on the given information. The expression for linear momentum does not directly provide information about the dependence of force on time, velocity on time, or displacement on time.
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The linear momentum of a particle varies with time t as p = a + bt + c...
As ...force = dp/,dt hence f= b+2ct ....clearly it is time dependent
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The linear momentum of a particle varies with time t as p = a + bt + ct2. Which of the following statement is correct? a)force varies with time in a quadratic manner b)Force is time-dependent c)The velocity of the particle is proportional to time d)The displacement of the particle is proportional to t.Correct answer is option 'B'. Can you explain this answer?
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The linear momentum of a particle varies with time t as p = a + bt + ct2. Which of the following statement is correct? a)force varies with time in a quadratic manner b)Force is time-dependent c)The velocity of the particle is proportional to time d)The displacement of the particle is proportional to t.Correct answer is option 'B'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The linear momentum of a particle varies with time t as p = a + bt + ct2. Which of the following statement is correct? a)force varies with time in a quadratic manner b)Force is time-dependent c)The velocity of the particle is proportional to time d)The displacement of the particle is proportional to t.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The linear momentum of a particle varies with time t as p = a + bt + ct2. Which of the following statement is correct? a)force varies with time in a quadratic manner b)Force is time-dependent c)The velocity of the particle is proportional to time d)The displacement of the particle is proportional to t.Correct answer is option 'B'. Can you explain this answer?.
The linear momentum of a particle varies with time t as p = a + bt + ct2. Which of the following statement is correct? a)force varies with time in a quadratic manner b)Force is time-dependent c)The velocity of the particle is proportional to time d)The displacement of the particle is proportional to t.Correct answer is option 'B'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The linear momentum of a particle varies with time t as p = a + bt + ct2. Which of the following statement is correct? a)force varies with time in a quadratic manner b)Force is time-dependent c)The velocity of the particle is proportional to time d)The displacement of the particle is proportional to t.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The linear momentum of a particle varies with time t as p = a + bt + ct2. Which of the following statement is correct? a)force varies with time in a quadratic manner b)Force is time-dependent c)The velocity of the particle is proportional to time d)The displacement of the particle is proportional to t.Correct answer is option 'B'. Can you explain this answer?.
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