Physics Elasticity Question 154
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
[UPSEAT 2002]
Options:
A) 1.38 cm
B)3.5 cm
C) 1.75 cm
D) 2.45 cm
Show Answer
Answer:
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} $
Therefore $ 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 $
BETA
