Question

Two line segments AB and CD are taken. Initially, the points B & D are coincident. The line segment CD is rotated about point D such that D and B continue to be coincident till C coincides with A. The distance covered by C is $y$ and the angle subtended by CD with respect to starting point is $\theta$. If CD completes one full revolution about D, the distance travelled would be $x$. Find the relation among $x$,$y$ and $\theta$. Assume that $\theta$ is in degrees.

• A. x = (y × θ)/360
• B. x = (y × θ)/180
• C. y = (x × θ)/360
• D. y = (x × θ)/260

Answer 1

The correct option is C

y = (x × θ)/360

We can see that if CD makes one full revolution, C covers the circumference of the circle which is given by $x$.

One full revolution is ${360}^{\circ }$ of the angular displacement. For an angular displacement of $\theta$¸ the movement of C is $y$.

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

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