Class 11 Exam > Class 11 Questions > The time dependence of a physical quantity ?P...
Start Learning for Free
The time dependence of a physical quantity ?
P = P0exp(_at2)
where a is a constant and t is time
The constant a
- a)Will be dimensionless
- b)Will have dimensions of T_2
- c)Will have dimensions as that of P
- d)Will have dimensions equal to the dimension of P multiplied by T_2
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The time dependence of a physical quantity ?P = P0exp(_at2)where a is ...
Given:
The time dependence of physical quantity P is found to be of the form
p=poexp(-α t2)
αt2 is dimensionless
Therefore:
α=1/t2
=1/[T2]
=[T-2] or[T^-2]
Conclusion :
constant α will [T-2] or[T^-2]
Most Upvoted Answer
The time dependence of a physical quantity ?P = P0exp(_at2)where a is ...
Dimensional Analysis of the given quantity:
?P = P0exp(_at2)
Here, P0 is the initial value of P.
Let's determine the dimensions of the various quantities involved in the expression:
Dimensions of P0 = [P]
Dimensions of t = [T]
Dimensions of ?P = [P]
Dimensions of a = [?P/T2]
Since the exponential function is dimensionless, the dimensions of the right-hand side of the equation will be the same as the dimensions of P0.
Therefore, [?P] = [P] = M^L^T^-2
Now, substituting the dimensions of ?P and a in the given equation:
[P] = [P0][exp(-[?P/T2][T^2])]
[P] = [P0][exp(-[?P][T^-1])]
[P] = [P0][exp(-[M^L^T^-2][T^-1])]
[P] = [P0][exp(-L^2/T)]
From the above equation, it is clear that the dimensions of the constant 'a' are the same as the dimensions of T^-2, i.e., T^2.
Therefore, option B is the correct answer.
?P = P0exp(_at2)
Here, P0 is the initial value of P.
Let's determine the dimensions of the various quantities involved in the expression:
Dimensions of P0 = [P]
Dimensions of t = [T]
Dimensions of ?P = [P]
Dimensions of a = [?P/T2]
Since the exponential function is dimensionless, the dimensions of the right-hand side of the equation will be the same as the dimensions of P0.
Therefore, [?P] = [P] = M^L^T^-2
Now, substituting the dimensions of ?P and a in the given equation:
[P] = [P0][exp(-[?P/T2][T^2])]
[P] = [P0][exp(-[?P][T^-1])]
[P] = [P0][exp(-[M^L^T^-2][T^-1])]
[P] = [P0][exp(-L^2/T)]
From the above equation, it is clear that the dimensions of the constant 'a' are the same as the dimensions of T^-2, i.e., T^2.
Therefore, option B is the correct answer.
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
|
Explore Courses for Class 11 exam
|
|
Top Courses for Class 11View all
The time dependence of a physical quantity ?P = P0exp(_at2)where a is a constant and t is timeThe constant aa)Will be dimensionlessb)Will have dimensions of T_2c)Will have dimensions as that of Pd)Will have dimensions equal to the dimension of P multiplied by T_2Correct answer is option 'B'. Can you explain this answer?
Question Description
The time dependence of a physical quantity ?P = P0exp(_at2)where a is a constant and t is timeThe constant aa)Will be dimensionlessb)Will have dimensions of T_2c)Will have dimensions as that of Pd)Will have dimensions equal to the dimension of P multiplied by T_2Correct 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 time dependence of a physical quantity ?P = P0exp(_at2)where a is a constant and t is timeThe constant aa)Will be dimensionlessb)Will have dimensions of T_2c)Will have dimensions as that of Pd)Will have dimensions equal to the dimension of P multiplied by T_2Correct 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 time dependence of a physical quantity ?P = P0exp(_at2)where a is a constant and t is timeThe constant aa)Will be dimensionlessb)Will have dimensions of T_2c)Will have dimensions as that of Pd)Will have dimensions equal to the dimension of P multiplied by T_2Correct answer is option 'B'. Can you explain this answer?.
The time dependence of a physical quantity ?P = P0exp(_at2)where a is a constant and t is timeThe constant aa)Will be dimensionlessb)Will have dimensions of T_2c)Will have dimensions as that of Pd)Will have dimensions equal to the dimension of P multiplied by T_2Correct 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 time dependence of a physical quantity ?P = P0exp(_at2)where a is a constant and t is timeThe constant aa)Will be dimensionlessb)Will have dimensions of T_2c)Will have dimensions as that of Pd)Will have dimensions equal to the dimension of P multiplied by T_2Correct 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 time dependence of a physical quantity ?P = P0exp(_at2)where a is a constant and t is timeThe constant aa)Will be dimensionlessb)Will have dimensions of T_2c)Will have dimensions as that of Pd)Will have dimensions equal to the dimension of P multiplied by T_2Correct answer is option 'B'. Can you explain this answer?.
Solutions for The time dependence of a physical quantity ?P = P0exp(_at2)where a is a constant and t is timeThe constant aa)Will be dimensionlessb)Will have dimensions of T_2c)Will have dimensions as that of Pd)Will have dimensions equal to the dimension of P multiplied by T_2Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 11.
Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of The time dependence of a physical quantity ?P = P0exp(_at2)where a is a constant and t is timeThe constant aa)Will be dimensionlessb)Will have dimensions of T_2c)Will have dimensions as that of Pd)Will have dimensions equal to the dimension of P multiplied by T_2Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The time dependence of a physical quantity ?P = P0exp(_at2)where a is a constant and t is timeThe constant aa)Will be dimensionlessb)Will have dimensions of T_2c)Will have dimensions as that of Pd)Will have dimensions equal to the dimension of P multiplied by T_2Correct answer is option 'B'. Can you explain this answer?, a detailed solution for The time dependence of a physical quantity ?P = P0exp(_at2)where a is a constant and t is timeThe constant aa)Will be dimensionlessb)Will have dimensions of T_2c)Will have dimensions as that of Pd)Will have dimensions equal to the dimension of P multiplied by T_2Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of The time dependence of a physical quantity ?P = P0exp(_at2)where a is a constant and t is timeThe constant aa)Will be dimensionlessb)Will have dimensions of T_2c)Will have dimensions as that of Pd)Will have dimensions equal to the dimension of P multiplied by T_2Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The time dependence of a physical quantity ?P = P0exp(_at2)where a is a constant and t is timeThe constant aa)Will be dimensionlessb)Will have dimensions of T_2c)Will have dimensions as that of Pd)Will have dimensions equal to the dimension of P multiplied by T_2Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup