Which of the following shows the dimensions of force and acceleration respectively?
Correct answer: D. MLT-2 and LT-1
- A. MLT-2 and LT-2
- B. ML2 T and LT-2
- C. MLT-2 and LT2
- D. MLT-2 and LT-1
Explanation
Force (F) is defined by Newton's second law as mass (m) multiplied by acceleration (a) (F = ma).* The dimension of mass is [M] (Mass).* The dimension of acceleration is [L][T]^-2 (Length per time squared).Therefore, the dimension of Force is [M][L][T]^-2.Dimensions of Acceleration:Acceleration (a) is the rate of change of velocity, which is velocity per unit time. Velocity is defined as displacement per unit time.* The dimension of displacement (length) is [L].* The dimension of time is [T].* So, the dimension of velocity is [L][T]^-1.* Therefore, the dimension of acceleration is [L][T]^-1 / [T] = [L][T]^-2.
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About Dimensional Analysis
Dimensional analysis expresses physical quantities through fundamental dimensions such as mass, length and time. It checks dimensional consistency, helps derive relations and converts between unit systems, but cannot determine numerical constants or distinguish quantities with identical dimensions. Dimensional formulae must not be confused with complete physical units.
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