A) 1.38 cm
B) 3.5 cm
C) 1.75 cm
D) 2.45 cm
Correct Answer: B
Solution :
\[2\pi \sqrt{\frac{m}{k}}=0.6\] ?(i) and \[2\pi \sqrt{\frac{m+m'}{k}}=0.7\] ?(ii) Dividing (ii) by (i) we get \[{{\left( \frac{7}{6} \right)}^{2}}=\frac{m+m'}{m}=\frac{49}{36}\] \[\frac{m+m'}{m}-1=\frac{49}{36}-1\Rightarrow \frac{m'}{m}=\frac{13}{36}\]Þ \[m'=\frac{13m}{36}\] Also \[\frac{k}{m}=\frac{4{{\pi }^{2}}}{{{(0.6)}^{2}}}\] Desired extension\[=\frac{m'g}{k}\]\[=\frac{13}{36}\times \frac{mg}{k}\] \[=\frac{13}{36}\times 10\times \frac{0.36}{4{{\pi }^{2}}}\approx 3.5\ cm\]
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