Applications Of Derivatives Question 356
Question: A 10cm 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 $ 2cm/\sec $ , then when the distance of A from O is $ 8cm $ , the rate at which the end B is moving, is
[SCRA 1996]
Options:
A) $ \frac{8}{3}cm/\sec $
B) $ \frac{4}{3}cm/\sec $
C) $ \frac{2}{9}cm/\sec $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
By figure, $ x^{2}+y^{2}=100 $ …..(i)
$ \Rightarrow 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 . $
$ =\frac{8}{3}cm/\sec $ .
BETA
