If y denotes force and x represents velocity, the dimensions of —=r are dx2__________________?
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Answer: B. M’L-‘T0
Explanation
Dimensional analysis of the ratio involving force and velocity derivatives yields the specific dimensional formula. Force has dimensions of mass multiplied by length divided by time squared, represented fundamentally as M L T^-2. Dividing the derivative of force with respect to velocity results in the precise dimensional expression matching option B. Dimensional analysis is a powerful problem-solving tool used in physics and engineering to check equations and convert units between different measurement systems. Fundamental physical dimensions include mass represented by M, length represented by L, and time represented by T. Derivatives in dimensional equations represent the rate of change of a physical quantity with respect to another changing variable.
Option A features an incorrect combination of exponents that does not properly reflect the fundamental dimensions of force and velocity derivatives. Option C contains a time exponent that fails to match the correct mathematical outcome of the dimensional ratio calculation. Option D introduces high mass and time exponents that are completely inconsistent with basic Newtonian mechanics and unit derivations.
- Subject
- Engineering
- Category
- Civil Engineering
- Topic
- —
- Difficulty
- medium
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