Question

A 10 cm long rod AB moves with its ends on two mutually perpendicular straight lines OX and OY. If the end A be moving at the rate of 2 cm/sec. then when the distance of A from O is 8 cm, the rate at which the end B is moving, is

• A. $\frac{8}{3}$ cm/sec
• B. $\frac{4}{3}cm/\sec$
• C. $\frac{2}{9}cm/sec.$
• D. None

Answer 1

Answer: (A)

$\frac{8}{3}$ cm/sec

Answer 2

By figure, $x^{2} + y^{2} = 100$ ......(i)

⇒ $2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0$ .....(ii)

$x = 8$

Therefore by (i) and (ii), $\frac{dy}{dt} = - \frac{16}{6} = - \frac{8}{3}cm/sec.$

$\therefore$ B is moving at the rate $\frac{8}{3}cm/sec.$