b
Work done in changing the orientation of a magnetic needle of magnetic moment \(M\) in a magnetic field \(B\) from position \(\theta_{1}\) to \(\theta_{2}\) is given by

\(W=M B\left(\cos \theta_{1}-\cos \theta_{2}\right)\)

Here, \(\theta_{1}=0^{\circ}, \theta_{2}=60^{\circ}\)

\(=M B\left(1-\frac{1}{2}\right)=\frac{M B}{2}.........(i)\)

The torque on the needle is

\(\vec{\tau}=\vec{M} \times \vec{B}\)

In magnitude,

\(\tau=M B \sin \theta=M B \sin 60^{\circ}=\frac{\sqrt{3}}{2} M B.........(ii)\)

Dividing \((ii)\) by \((i)\), we get

\(\frac{\tau }{W} = \sqrt 3 \)

\(\tau  = \sqrt 3 W = \sqrt 3  \times \sqrt 3 \,{\text{J}} = 3\,{\text{J}}\)