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In terms of time t and distance x ,the force F is given by F=A sin ct B cos D x, then dimensions of A/B and C/D?
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In terms of time t and distance x ,the force F is given by F=A sin ct ...
Dimensions of A/B and C/D in Force Equation
Understanding the Force Equation:
- The force F is given by F = A sin(ct) + B cos(Dx), where A, B, c, and D are constants.
Dimensions of A/B:
- The dimensions of A and B can be determined by analyzing the dimensions of the force equation.
- The dimensions of force (F) are given by [M L T^-2].
- The dimensions of sin(ct) and cos(Dx) are dimensionless.
- Therefore, the dimensions of A and B must be [M L T^-2].
Dimensions of C/D:
- The constants c and D in the force equation are related to the time (t) and distance (x) variables, respectively.
- The dimensions of ct are [T] (time) and the dimensions of Dx are [L] (length).
- Since sin(ct) and cos(Dx) are dimensionless, the dimensions of c and D must be reciprocal to the dimensions of time and length, respectively.
- Therefore, the dimensions of c are [T^-1] and the dimensions of D are [L^-1].
In conclusion, the dimensions of A and B are [M L T^-2], and the dimensions of c and D are [T^-1] and [L^-1], respectively, based on the force equation F = A sin(ct) + B cos(Dx).
Understanding the Force Equation:
- The force F is given by F = A sin(ct) + B cos(Dx), where A, B, c, and D are constants.
Dimensions of A/B:
- The dimensions of A and B can be determined by analyzing the dimensions of the force equation.
- The dimensions of force (F) are given by [M L T^-2].
- The dimensions of sin(ct) and cos(Dx) are dimensionless.
- Therefore, the dimensions of A and B must be [M L T^-2].
Dimensions of C/D:
- The constants c and D in the force equation are related to the time (t) and distance (x) variables, respectively.
- The dimensions of ct are [T] (time) and the dimensions of Dx are [L] (length).
- Since sin(ct) and cos(Dx) are dimensionless, the dimensions of c and D must be reciprocal to the dimensions of time and length, respectively.
- Therefore, the dimensions of c are [T^-1] and the dimensions of D are [L^-1].
In conclusion, the dimensions of A and B are [M L T^-2], and the dimensions of c and D are [T^-1] and [L^-1], respectively, based on the force equation F = A sin(ct) + B cos(Dx).
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In terms of time t and distance x ,the force F is given by F=A sin ct B cos D x, then dimensions of A/B and C/D?
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In terms of time t and distance x ,the force F is given by F=A sin ct B cos D x, then dimensions of A/B and C/D? 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 In terms of time t and distance x ,the force F is given by F=A sin ct B cos D x, then dimensions of A/B and C/D? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In terms of time t and distance x ,the force F is given by F=A sin ct B cos D x, then dimensions of A/B and C/D?.
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