question_answer

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]

A)            \[\frac{8}{3}cm/\sec \]

B)            \[\frac{4}{3}cm/\sec \]

C)            \[\frac{2}{9}cm/\sec \]

D)            None of these

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),                     \[\frac{dy}{dt}=-\frac{16}{6}=-\frac{8}{3}cm/\sec .\]                          \[=\frac{8}{3}cm/\sec \].