Question

A force, $F$ when applied to the end of a wrench of length, $l$ at an angle of ${90}^o$ generates a torque, $\tau$.
At what angle would this same force, $F$ produce a torque $\frac{\tau }{2}$?

• A. $0^o$
• B. ${30}^o$
• C. ${45}^o$
• D. ${60}^o$
• E. ${\frac{1}{2}}^o$

Answer 1

Answer: (B)

${30}^o$

Torque about a point $\tau =lF$ $sin\theta$ where $\theta$ is the angle between $r$ and $F$

Case 1 : $\theta ={90}^o$

$\therefore$ $\tau =lF$ .............(1)

Case 2 : ${\tau }^{\prime }=\frac{\tau }{2}$

$\therefore$ $\frac{\tau }{2}=lF$ $sin\theta$

OR $\frac{\tau }{2}=\tau$ $sin\theta$

$\therefore$ $sin\theta =0.5$ $⟹\theta ={30}^o$