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
Text Solution
Verified by ExpertsB
$2 \pi \sqrt{\frac{m}{k}} = 0.6$ …(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 $= \frac{m'/g}{k} = \frac{13}{36} \times \frac{mg}{k}$ $= \frac{13}{36} \times 10 \times \frac{0.36}{4 \pi^2} \approx 3.5 \text{ cm}$
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems