Question

A force is applied on a door at point P making an angle $\theta$ with position vector $\overline{r}$, by partical observation, give the value of $\theta$ for which on has to exert minimum force to rotate the door ?

• A. $0^o$
• B. $\pi$
• C. $\frac{\pi }{2}$
• D. $\frac{\pi }{3}$

Answer 1

Answer: (C)

$\frac{\pi }{2}$

$\begin{array}{c}\text{* Force apblied on a Point}P\text{with position vector}\overrightarrow{r}\\ \text{at an angle theta-}\\ \text{To Rotate the door the torque must be maximum}\\ \text{Let a force}F\text{is applied on the door then-}\end{array}$

$\begin{array}{c}\text{torque -}\\ \tau =\overrightarrow{r}\times \overrightarrow{F}=|F\cdot |\cdot |r|\cdot \sin \theta \\ \text{For torque to be maximum sintheta must be maximum}\\ \text{Henee}\sin \theta \text{max. value is obtained when}\\ \theta =\pi /2\\ \text{Hence, option (c) is correct.}\end{array}$