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Dimensional Formula:
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Acceleration due to gravity (g) is the acceleration gained by an object due to gravitational force. On Earth's surface, its standard value is approximately 9.8 m/s². It represents the rate at which an object's velocity changes under the influence of gravity alone.
The dimensional formula expresses the physical quantity in terms of fundamental dimensions:
Where:
Explanation: Acceleration is defined as the rate of change of velocity with time. Since velocity has dimensions L T⁻¹, acceleration becomes (L T⁻¹) T⁻¹ = L T⁻².
Method: The dimensional formula is derived from the definition of acceleration: g = Δv/Δt, where velocity v has dimensions L T⁻¹ and time t has dimensions T.
Details: Dimensional analysis is used to check the consistency of equations, derive relationships between physical quantities, and convert units between different systems of measurement.
Q1: Why is the time dimension negative in the formula?
A: The negative exponent indicates that as time increases in the denominator, the quantity decreases. Acceleration has time squared in the denominator (m/s²).
Q2: What are the fundamental dimensions in physics?
A: The seven fundamental dimensions are: Length (L), Mass (M), Time (T), Electric Current (I), Temperature (Θ), Amount of Substance (N), and Luminous Intensity (J).
Q3: How does g vary with location?
A: Acceleration due to gravity varies with altitude, latitude, and local geological formations, but its dimensional formula remains constant.
Q4: Can dimensional analysis prove an equation is correct?
A: Dimensional analysis can only prove an equation is dimensionally consistent, not necessarily physically correct. It's a necessary but not sufficient condition.
Q5: What is the difference between dimensional formula and units?
A: Dimensional formula shows the fundamental dimensions involved, while units are specific measurement standards (e.g., meters, seconds, feet, etc.).