The question asks for the fundamental (base) unit of mass in the International System of Units (SI). This requires knowledge of the SI base units.
B) Kilogram is the SI fundamental (base) unit of mass. It is one of the seven base units of the SI system.
The question asks to identify a derived physical quantity among the given options. We need to understand the difference between fundamental (base) and derived quantities in the SI system.
C) Force is a derived quantity. It is defined as mass times acceleration (\(F = ma\)). Since mass is a fundamental quantity and acceleration is derived from length and time (both fundamental quantities), force is a derived quantity.
To find the dimensional formula for force, we start with Newton's second law of motion, which defines force in terms of mass and acceleration. Then, we break down acceleration into its fundamental dimensions of length and time.
This is the correct dimensional formula for force.
Correct Option: B) The dimensional formula for force is \([M^1L^1T^{-2}]\). This is derived directly from Newton's second law, \(F = ma\), where \(m\) has dimensions of \([M]\) and \(a\) (acceleration) has dimensions of \([LT^{-2}]\).
To determine which physical quantity is a vector, we need to understand the definitions of scalar and vector quantities. A scalar quantity has only magnitude, while a vector quantity has both magnitude and direction.
Correct Option: B) Displacement is a vector quantity because it possesses both magnitude and direction.
The question asks for the key difference between distance and displacement. To answer this, we need to understand the definitions of both terms, particularly their nature as scalar or vector quantities and how they are calculated.
C) Distance is the total path length travelled (scalar); displacement is the shortest straight-line distance between initial and final positions (vector). This option accurately captures the definitions and the scalar/vector nature of both quantities. Distance measures the actual path covered, while displacement measures the net change in position.
The principle of homogeneity of dimensions is a fundamental concept in physics used to check the consistency of equations. It states a specific rule about how physical quantities with different dimensions can interact mathematically.
Correct Option: C) Only quantities having the same dimensions can be added, subtracted, or equated.