Question

Equation of the hour hand at $4$ O’ clock is

• A. $x-\sqrt{3}y=0$
• B. $\sqrt{3}x-y=0$
• C. $x+\sqrt{3}y=0$
• D. $\sqrt{3}x+y=0$

Answer 1

The correct option is C $x+\sqrt{3}y=0$

Since the hour, minute and second hands always pass through origin because one end of these hands is always at origin. Now at $4$ O' clock, the hour hand makes ${30}^{\circ }$ angle in fourth quadrant. So the equation of hour hand is


$y=mx\Rightarrow y=-\frac{1}{\sqrt{3}}x$
[Since, slope $m=\tan (-{30}^{\circ })=\frac{-1}{\sqrt{(}3)}$]
$\therefore x+\sqrt{3}y=0$ is the required equation.