A pan with set of weights is attached with a light spring. When d… - Vidyadip

MCQ

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
$1.38 cm$
✓
$3.5 cm$
C
$1.75 cm$
D
$2.45 cm$

✓

Answer

Correct option: B.

$3.5 cm$

$2 \pi \sqrt{\frac{m}{k}}=0.6 \quad \ldots(\mathrm{i})$ and $2 \pi\sqrt{\frac{m+m^{\prime}}{k}}=0.7$
Dividing (ii) by (i) we get $\left(\frac{7}{6}\right)^2=\frac{m+m^{\prime}}{m}=\frac{49}{36}$
$\frac{m+m^{\prime}}{m}-1=\frac{49}{36}-1 \Rightarrow \frac{m^{\prime}}{m}=\frac{13}{36} \Rightarrow m^{\prime}=\frac{13 m}{36}$
Also $\frac{k}{m}=\frac{4 \pi^2}{(0.6)^2}$
Desired extension $=\frac{m^{\prime} g}{k}=\frac{13}{36} \times \frac{m g}{k}$
$=\frac{13}{36} \times 10 \times \frac{0.36}{4 \pi^2} \approx 3.5 \mathrm{~cm}$

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