A thin straight bar magnet has a magnetic moment M . It is bent at...

Let the initial length of the bar magnet be $L$ and its pole strength be $m$.

The initial magnetic moment is $M = m \times L$.

When the magnet is bent at its midpoint, each half has a length of $\dfrac{L}{2}$.

The angle between the two halves is $60^{\circ}$.

The new effective magnetic length $L^{\prime}$ is the shortest straight-line distance between the two poles.

The two halves and the line joining the poles form a triangle with two equal sides ($\dfrac{L}{2}$) and an included angle of $60^{\circ}$. This geometry forms an equilateral triangle.

Therefore, the distance between the poles is $L^{\prime} = \dfrac{L}{2}$.

The new magnetic moment is $M^{\prime} = m \times L^{\prime} = m \times \left(\dfrac{L}{2}\right) = \dfrac{M}{2}$.

Answer: $\dfrac{M}{2}$