If the length of an arc of a circle of radius $r$ is equal to that of an arc of a circle of radius $2r$,then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle. Is this statement false? Why?

(A) The statement is true,not false.
Let two circles $C_1$ and $C_2$ have radii $r$ and $2r$ with centers $O$ and $O'$,respectively.
It is given that the arc length $l_1$ of $C_1$ is equal to the arc length $l_2$ of $C_2$,i.e.,$l_1 = l_2 = l$.
Let $\theta_1$ be the angle subtended by the arc of $C_1$ and $\theta_2$ be the angle subtended by the arc of $C_2$ at their respective centers.
The formula for arc length is $l = \frac{\theta}{360^\circ} \times 2\pi R$.
For $C_1$: $l = \frac{\theta_1}{360^\circ} \times 2\pi r$ ........... $(i)$
For $C_2$: $l = \frac{\theta_2}{360^\circ} \times 2\pi(2r) = \frac{\theta_2}{360^\circ} \times 4\pi r$ ........... $(ii)$
Equating $(i)$ and $(ii)$:
$\frac{\theta_1}{360^\circ} \times 2\pi r = \frac{\theta_2}{360^\circ} \times 4\pi r$
$\theta_1 = 2\theta_2$
Thus,the angle of the sector of the first circle is double the angle of the sector of the second circle. Therefore,the statement is true.