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Force F is given in terms of time t and distance x byF = A sin C t + B cos D xThen the dimensions ofA/B andC/D are given byA :MLT_2, M0L0T_1B :MLT_2, M0L_1T0C :M0L0T0, M0L1T_1D :M0L1T_1, M0L0T0
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Force F is given in terms of time t and distance x byF = A sin C t + B...
Dimensions of A/B:
- Force F is given by F = A sin(Ct) B cos(Dx)
- A represents the amplitude of the sine wave and B represents the amplitude of the cosine wave
- The dimensions of A can be derived as follows:
- F = MA/LT^2 (force)
- sin(Ct) = dimensionless
- A = F/sin(Ct) = MA/LT^2 (amplitude)
- The dimensions of B can be derived as follows:
- F = MA/LT^2 (force)
- cos(Dx) = dimensionless
- B = F/cos(Dx) = MA/LT^2 (amplitude)
Dimensions of C/D:
- The dimensions of C can be derived as follows:
- F = MA/LT^2 (force)
- sin(Ct) = dimensionless
- C = 1/t = T^-1 (frequency)
- Therefore, CT = 1, and the dimensions of C are M^0L^0T^-1
- The dimensions of D can be derived as follows:
- F = MA/LT^2 (force)
- cos(Dx) = dimensionless
- D = 1/x (wavenumber)
- Therefore, DX = 1, and the dimensions of D are M^0L^-1T^-1
In summary, the dimensions of A and B are both MLT^-2, and the dimensions of C and D are M^0L^0T^-1 and M^0L^-1T^-1, respectively.
- Force F is given by F = A sin(Ct) B cos(Dx)
- A represents the amplitude of the sine wave and B represents the amplitude of the cosine wave
- The dimensions of A can be derived as follows:
- F = MA/LT^2 (force)
- sin(Ct) = dimensionless
- A = F/sin(Ct) = MA/LT^2 (amplitude)
- The dimensions of B can be derived as follows:
- F = MA/LT^2 (force)
- cos(Dx) = dimensionless
- B = F/cos(Dx) = MA/LT^2 (amplitude)
Dimensions of C/D:
- The dimensions of C can be derived as follows:
- F = MA/LT^2 (force)
- sin(Ct) = dimensionless
- C = 1/t = T^-1 (frequency)
- Therefore, CT = 1, and the dimensions of C are M^0L^0T^-1
- The dimensions of D can be derived as follows:
- F = MA/LT^2 (force)
- cos(Dx) = dimensionless
- D = 1/x (wavenumber)
- Therefore, DX = 1, and the dimensions of D are M^0L^-1T^-1
In summary, the dimensions of A and B are both MLT^-2, and the dimensions of C and D are M^0L^0T^-1 and M^0L^-1T^-1, respectively.
Community Answer
Force F is given in terms of time t and distance x byF = A sin C t + B...
AsinCt=BcosDx= Force {same quantities can be added or subtracted}
In SinCt is angle so dimension of C= 1/t.
cosDx ; dimensions of D=1/x.
A and B have same dimensions as Force.
Since AsinCt =Force; sinCt has dimension=1 so A =Force.
so A/B= Force/Force= M0L0T0
C/D=x/t= M0L1T-1 Option C is correct answer
In SinCt is angle so dimension of C= 1/t.
cosDx ; dimensions of D=1/x.
A and B have same dimensions as Force.
Since AsinCt =Force; sinCt has dimension=1 so A =Force.
so A/B= Force/Force= M0L0T0
C/D=x/t= M0L1T-1 Option C is correct answer
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Force F is given in terms of time t and distance x byF = A sin C t + B cos D xThen the dimensions ofA/B andC/D are given byA :MLT_2, M0L0T_1B :MLT_2, M0L_1T0C :M0L0T0, M0L1T_1D :M0L1T_1, M0L0T0
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Force F is given in terms of time t and distance x byF = A sin C t + B cos D xThen the dimensions ofA/B andC/D are given byA :MLT_2, M0L0T_1B :MLT_2, M0L_1T0C :M0L0T0, M0L1T_1D :M0L1T_1, M0L0T0 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 Force F is given in terms of time t and distance x byF = A sin C t + B cos D xThen the dimensions ofA/B andC/D are given byA :MLT_2, M0L0T_1B :MLT_2, M0L_1T0C :M0L0T0, M0L1T_1D :M0L1T_1, M0L0T0 covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Force F is given in terms of time t and distance x byF = A sin C t + B cos D xThen the dimensions ofA/B andC/D are given byA :MLT_2, M0L0T_1B :MLT_2, M0L_1T0C :M0L0T0, M0L1T_1D :M0L1T_1, M0L0T0.
Force F is given in terms of time t and distance x byF = A sin C t + B cos D xThen the dimensions ofA/B andC/D are given byA :MLT_2, M0L0T_1B :MLT_2, M0L_1T0C :M0L0T0, M0L1T_1D :M0L1T_1, M0L0T0 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 Force F is given in terms of time t and distance x byF = A sin C t + B cos D xThen the dimensions ofA/B andC/D are given byA :MLT_2, M0L0T_1B :MLT_2, M0L_1T0C :M0L0T0, M0L1T_1D :M0L1T_1, M0L0T0 covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Force F is given in terms of time t and distance x byF = A sin C t + B cos D xThen the dimensions ofA/B andC/D are given byA :MLT_2, M0L0T_1B :MLT_2, M0L_1T0C :M0L0T0, M0L1T_1D :M0L1T_1, M0L0T0.
Solutions for Force F is given in terms of time t and distance x byF = A sin C t + B cos D xThen the dimensions ofA/B andC/D are given byA :MLT_2, M0L0T_1B :MLT_2, M0L_1T0C :M0L0T0, M0L1T_1D :M0L1T_1, M0L0T0 in English & in Hindi are available as part of our courses for Class 11.
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Force F is given in terms of time t and distance x byF = A sin C t + B cos D xThen the dimensions ofA/B andC/D are given byA :MLT_2, M0L0T_1B :MLT_2, M0L_1T0C :M0L0T0, M0L1T_1D :M0L1T_1, M0L0T0, a detailed solution for Force F is given in terms of time t and distance x byF = A sin C t + B cos D xThen the dimensions ofA/B andC/D are given byA :MLT_2, M0L0T_1B :MLT_2, M0L_1T0C :M0L0T0, M0L1T_1D :M0L1T_1, M0L0T0 has been provided alongside types of Force F is given in terms of time t and distance x byF = A sin C t + B cos D xThen the dimensions ofA/B andC/D are given byA :MLT_2, M0L0T_1B :MLT_2, M0L_1T0C :M0L0T0, M0L1T_1D :M0L1T_1, M0L0T0 theory, EduRev gives you an
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