Q. A pan with set of weights is attached with a light spring. When disturbed, the mass-spring system oscillates with a time period of $0.6\ s$. When some additional weights are added then time period is $0.7\ s$. The extension caused by the additional weights is approximately given by
A) $1.38\ cm$
B) $3.5\ cm$
C) $1.75\ cm$
D) $2.45\ cm$
Explanation
(b) $2\pi\sqrt{\frac{m}{k}} = 0.6$ …(i) and $2\pi\sqrt{\frac{m + m^{'}}{k}} = 0.7$ …(ii)
Dividing (ii) by (i), we get $\left( \frac{7}{6} \right)^{2} = \frac{m + m^{'}}{m} = \frac{49}{36}$
$\frac{m + m'}{m} - 1 = \frac{49}{36} - 1 \Rightarrow \frac{m^{'}}{m} = \frac{13}{36}$
$\Rightarrow m^{'} = \frac{13m}{36}$
Also $\frac{k}{m} = \frac{4\pi^{2}}{(0.6)^{2}}$
Desired extension $= \frac{m^{'}g}{k} = \frac{13}{36} \times \frac{mg}{k}$
$\frac{13}{36} \times 10 \times \frac{0.36}{4\pi^{2}} = 3.5\ cm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.