Physics - NLM Question with Solution | TestHub

To maintain equilibrium, the force from balance C must be equal and opposite to the resultant of forces from A and B. Since A and B are at $90^{\circ }$, the resultant force $R=\sqrt{F_A^2+F_B^2}=\sqrt{5^2+12^2}=\sqrt{25+144}=\sqrt{169}=13$ N. Thus, the reading on balance C is 13 N.

The angle $\theta$ with respect to balance B is given by $\tan \theta =\frac{F_A}{F_B}=\frac{5}{12}$.

$\theta =\arctan (\frac{5}{12})\approx 22.6^{\circ }$.

The angle with respect to balance A is $90^{\circ }-22.6^{\circ }=67.4^{\circ }$.

The angle $\theta$ in the figure is measured from the horizontal (balance A). Therefore, $\theta =67.4^{\circ }$.

The final answer is $\boxed{A}$.