## College Physics (4th Edition)

The correct answer is (d) $1/\sqrt{2}$
The area of the original circle is $A = \pi r^2$ We multiply the radius $r$ by some factor $k$; The new radius is $kr$. The area of the new circle is $A_2 = \pi (kr)^2$ We know that $A_2 = \frac{A}{2}$ $\pi (kr)^2 = \frac{\pi r^2}{2}$ $k^2 \pi r^2 = \frac{\pi r^2}{2}$ $k^2 = \frac{1}{2}$ $k = \sqrt{\frac{1}{2}} = 1 / \sqrt{2}$ The correct answer is (d) $1/\sqrt{2}$