Check the Correctness of Formula Where T is The Time Period and k is The Force Per Unit Displacement.
Check the correctness of formula where T is the time period and k is the force per unit displacement is an important numerical based question from Simple Harmonic Motion which we verify using dimensional analysis step by step.
Meaning of Time Period
Time period (T) is defined as the time taken in one complete oscillation. It is measured in seconds.
Meaning of Force Per Unit Displacement (k)
Force per unit displacement is known as spring constant in SHM and is measured in Newton per meter (N/m).
Dimensional Formula and Correctness
To check correctness, we compare dimensions of Left Hand Side (Time period) and Right Hand Side (formula). If both match, the formula is dimensionally correct.
- Time period dimension → [T]
- Spring constant dimension → [M T⁻²]
- Using formula, dimension becomes equal to [T]
Note: A formula may be dimensionally correct but physically incorrect. Dimensional method only gives correctness of units, not theory.
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