First slide

Elastic behaviour of solids

Question

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 0.7s. The extension caused by the additional weights is approximately given by

Moderate

A

1.38 cm
B

3.5 cm
C

1.75 cm
D

2.45 cm

Solution

$2 π \sqrt{\frac{m}{k}} = 0 .6 \dots ..(i) and 2 π \sqrt{\frac{m + m^{'}}{k}} = 0.7 . . . . . . . . (ii)$
Dividing (ii) by (i), we get ${(\frac{7}{6})}^{2} = \frac{m + m^{'}}{m} = \frac{49}{36}$
$\frac{m + m^{'}}{m} - 1 = \frac{49}{36} - 1 \Rightarrow \frac{m^{'}}{m} = \frac{13}{36} \Rightarrow m^{'} = \frac{13 m}{36}$
$Also \frac{k}{m} = \frac{4 π^{2}}{(0 .6)^{2}}$
$Desired extension = \frac{m^{'} g}{k} = \frac{13}{36} \times \frac{mg}{k}$
$= \frac{13}{36} \times 10 \times \frac{0 .36}{4 π^{2}} \approx 3 .5 cm$

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