Two long bar magnets are positioned such that their axes coincide...

Since the magnets are long, the force between them is predominantly due to their adjacent poles. The effect of the farther poles can be neglected.

The force between two magnetic poles is given by Coulomb's law for magnetism:

$F = \dfrac{\mu_0}{4\pi} \dfrac{m_1 m_2}{r^2}$

Given:
Pole strength, $m_1 = m_2 = 10 \text{ Am}$
Distance between the adjacent poles, $r = 2.0 \text{ cm} = 0.02 \text{ m}$
Constant, $\dfrac{\mu_0}{4\pi} = 10^{-7} \text{ N A}^{-2}$

Substituting the values into the formula:

$F = 10^{-7} \times \dfrac{10 \times 10}{(0.02)^2}$

$F = 10^{-7} \times \dfrac{100}{4 \times 10^{-4}}$

$F = 10^{-7} \times 25 \times 10^4$

$F = 25 \times 10^{-3} \text{ N} = 0.025 \text{ N}$