A) \[3\,\,W\]
B) \[\sqrt{3}\,\,W\]
C) \[\frac{W}{3}\]
D) \[\frac{W}{\sqrt{3}}\]
Correct Answer: B
Solution :
The instaneous moment of the deflecting couple or torque acting on the needle is \[\tau =\text{force}\times \text{perpendicular}\,\text{distance}=\text{work done}\]when axis of needle makes an angle \[\theta \] with the magnetic field, then for magnetic moment \[M\] and magnetic field\[B\], we have \[\tau =MB\,\,\sin \,\theta \] ?(1) \[W=MB\,\,\cos \,\theta \] ?(2) Dividing Eq. (1) by Eq. (2), we get \[\frac{\tau }{W}=\frac{MB\,\,\sin \,\,\theta }{MB\,\,\cos \,\,\theta }\] Given, \[\theta ={{60}^{\circ }}\] \[\tau =W\frac{\sin \,\,{{60}^{\circ }}}{\cos \,\,{{60}^{\circ }}}\] \[W=\sqrt{3}\]
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