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A spring is hanging down from the ceiling, and an object of mass m is attached to the free end. The object is pulled down, thereby stretching the spring, and then released. The object oscillates up and down, and the time T required for one complete up-and-down oscillation is given by the equation , where k is known as the spring constant. What must be the dimension of k for this equation to be dimensionally correct

Respuesta :

Answer:

Explanation:

We know that

[tex]T=2\pi\sqrt{\frac{m}{k} }[/tex]

TĀ² = 4Ļ€Ā² m / k

k = Ā 4Ļ€Ā² m / TĀ²

Putting the dimension on the right hand side

k = M / TĀ² = MLTā»Ā² / L = Force / length = N / m

So dimension of k = MTā»Ā² and unit will be N/m .

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