Question

Two line segments AB and CD are taken. Initially, the points A & C and B & D are coincident. The line segment CD is rotated about point D such that CD coincides with AB again, when it covers a distance of $x$. If the distance covered by C is $y$, the angle subtended by CD with respect to starting point is $\theta$, then find the relation among $x$,$y$ and $\theta$. Assume that $\theta$ is in degrees.

• A. $x$ = $\frac{(y\times \theta )}{360}$
• B. $x$= $\frac{(y\times \theta )}{180}$
• C. y = $\frac{(x\times \theta )}{360}$
• D. y = $\frac{(x\times \theta )}{260}$

Answer 1

The correct option is C

y = $\frac{(x\times \theta )}{360}$

We can see that if CD traverses the circumference of the circle, when it covers a distance $x$ and the angular displacement will be ${360}^{\circ }$

(One full revolution is ${360}^{\circ }$ ) For an angular displacement of $\theta$¸ the distance covered by CD is $y$.

Hence, $x$ is proportional to ${360}^{\circ }$ and $y$ to $\theta$ degrees. Thus $\frac{x}{360}$ = $\frac{y}{\theta }$¸

So, $y$ = $\frac{(x\times \theta )}{360}$