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**Hint:**The geometric length of magnetic dipole is the measure of the total length of the magnet. The distance between the two magnetic poles is called the magnetic length. The shortest distance between the two poles is known as the effective length and it is less than the geometric length.

**Formula used:**

The formula of the geometric length is given by,

$ \Rightarrow G \cdot L = \dfrac{6}{5} \times M \cdot L$

Where geometric length is G.L and magnetic length is M.L.

**Complete step by step solution:**

When two opposite charged particles are situated at some distance then there is flow of magnetic field lines from the arrangement. The magnetic dipole moment is the magnetic strength of the magnetic dipole or magnet or any other substance that produces a magnetic field.

It is asked in the problem that a short magnetic dipole of magnetic length 10 cm then we need to find its geometric length.

The formula of the geometric length is given by,

$ \Rightarrow G \cdot L = \dfrac{6}{5} \times M \cdot L$

Where geometric length is G.L and magnetic length is M.L.

It is given in the problem that the magnetic length is 10 cm therefore we get,

$ \Rightarrow G \cdot L = \dfrac{6}{5} \times M \cdot L$

$ \Rightarrow G \cdot L = \dfrac{6}{5} \times 10$

$ \Rightarrow G \cdot L = 6 \times 2$

$ \Rightarrow G \cdot L = 12cm$

**The geometric length of the magnetic dipole is equal to 12 cm. The correct answer for this problem is option A.**

**Note:**The magnet has two poles namely South Pole and north pole also there is some distance between them and they are named as geometric length, magnetic length and effective length. The magnetic field is flowing from the north pole towards the south pole outside the magnet and inside the magnet the direction is from the south pole to north pole.

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