A rod AB, 10 feet long moves with its ends A and B on two perpendicular OX and OY respectively when A is 8 feet from 0, it is moving away at the rate of 2 feet/sec. At this instant B is moving at the rate.

$\frac{8}{3}$ $\frac{3}{8}$ $-\frac{8}{3}$ None of these

$-\frac{8}{3}$

OB = 6 $OA^2+OB^2=100$ $⇒2×OA\frac{d(OA)}{dt}+2×OB\frac{d(OB)}{dt}=0$ $⇒OA.V_A+OB.V_B=0$ $⇒V_B=-\frac{2×8}{6}=-\frac{8}{3}$ feet/s