A 10 ,cm long rod AB moves with its ends on two mutually perpendi… - Vidyadip

MCQ

$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

✓
${8 \over 3} \,cm/\sec $
B
${4 \over 3} \,cm/\sec $
C
${2 \over 9} \,cm/\sec $
D
None of these

✓

Answer

Correct option: A.

${8 \over 3} \,cm/\sec $

a
(a) 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 $.

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