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Test dimensionally if the formula t= 2 p...

Test dimensionally if the formula `t= 2 pi sqrt(m/(F/x))` may be corect where t is time period, F is force and x is distance.

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To test the dimensional correctness of the formula \( t = 2 \pi \sqrt{\frac{m}{\frac{F}{x}}} \), where \( t \) is the time period, \( F \) is the force, and \( x \) is the distance, we will follow these steps: ### Step 1: Identify the dimensions of each variable - **Time period \( t \)**: The dimension of time is denoted as \( [T] \). - **Mass \( m \)**: The dimension of mass is denoted as \( [M] \). - **Force \( F \)**: Force is defined as mass times acceleration. The dimension of acceleration is \( [L][T^{-2}] \). Therefore, the dimension of force is: \[ [F] = [M][L][T^{-2}] ...
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