A) 4 cm/s towards the mirror
B) 9 cm/s towards the mirror
C) 4 cm/s away from the mirror
D) 9 cm/s away from the mirror
Correct Answer: C
Solution :
[c] \[\frac{1}{u}+\frac{1}{v}=\frac{1}{f}\Rightarrow v=\frac{uf}{u-f}=\frac{60\times 24}{36}=40\text{cm}\] Further differentiation give, \[\frac{1}{{{u}^{2}}}\frac{du}{dt}+\frac{1}{{{v}^{2}}}\frac{dv}{dt}=0\] \[\Rightarrow \] \[\frac{dv}{dt}=-\frac{{{v}^{2}}}{{{u}^{2}}}\frac{du}{dt}=-{{\left( \frac{40}{60} \right)}^{2}}\times 9=-4\,\text{cm/s}\]
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