A) \[2.26\times {{10}^{-3}}m/s\] away from the lens
B) \[3.22\times {{10}^{-3}}m/s\] towards the lens
C) \[1.16\times {{10}^{-3}}m/s\] towards the lens
D) \[0.92\times {{10}^{-3}}m/s\] away from the lens
Correct Answer: C
Solution :
From the lens equation,\[\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\] ?.(1) \[\Rightarrow \frac{1}{v}=\frac{1}{0.3}+\frac{1}{-20}=\frac{197}{60}\Rightarrow v=\frac{60}{197}m\] Differentiating eqn. (i), \[0=-\frac{1}{{{v}^{2}}}\frac{dv}{dt}+\frac{1}{{{u}^{2}}}\frac{du}{dt}\] \[\Rightarrow \]\[{{\left( \frac{197}{60} \right)}^{2}}\frac{dv}{dt}=\frac{1}{{{20}^{2}}}(5)\] \[\Rightarrow \]\[\frac{dv}{dt}=1.16\times {{10}^{-3}}m/s\]
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