Question

Dimension of force constant is given by,​

Answer 1

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Spring Constant or force constant is defined as the applied force if the displacement in the spring is unity. It is denoted by k. The dimensional formula can be worked out by using the spring force formula i.e. F = kx . This gives k = F/x

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Answer 2

The dimensions of Force constant k is [MT⁻²]

Explanation:

Force F in spring extended by a length x is given by

$F=-kx$

According to the Newton's second law

$F=ma$

Where m is mass and a is acceleration

Thus we can write

$kx=ma$

$\implies k=\frac{ma}{x}$

$\implies \text{Dimensions of k}=\frac{\text{Dimension of m}\times\text{Dimensions of a}}{\text{Dimension of x}}$

$\implies \text{Dimensions of k}=\frac{[M][LT^{-2}]}{[L]}$

$\implies \text{Dimensions of k}=[MT^{-2}]$

Hope this answer is helpful.

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