question_answer

Forces 5 N, 12 N and 13 N are in equilibrium. If\[sin\text{ }23{}^\circ =\frac{5}{13},\]the angle between 5 N force and 13 N force is

A)  \[23{}^\circ \]                                  

B)  \[67{}^\circ \]   

C)  \[90{}^\circ \]                                  

D) \[113{}^\circ \]

Correct Answer: B

Solution :

                 As\[{{5}^{2}}+{{12}^{2}}={{13}^{2}},\] so these forces will be acting along the sides of a right angled triangle. Angle between 5 N and 13 N \[=180-(90+23)\] \[=180-113={{67}^{o}}\]