Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • A cylindrical piece of cork of density of base area A and height h floats in a liquid of density rho subscript imath. The cork is depressed slightly and then released

Q. 14.18 A cylindrical piece of cork of density of base area A and height h floats in a liquid of density \rho _{\imath }. The cork is depressed slightly and then released

Show that the cork oscillates up and down simple harmonically with a period   T=2\pi \sqrt{\frac{h\rho }{\rho _{ 1}g}} where \rho is the density of cork. (Ignore damping due to viscosity of the liquid).

Answers (1)

best_answer

Let the cork be displaced by a small distance x in downwards direction from its equilibrium position where it is floating.

The extra volume of fluid displaced by the cork is Ax

Taking the downwards direction as positive we have

\\ma=-\rho _{1}gAx\\ \rho Aha=-\rho _{1}gAx\\ \frac{\mathrm{d}^{2} x}{\mathrm{d} t^{2}}=-\frac{\rho _{1}g}{\rho h}x

Comparing with a=-kx we have

\\k=\frac{\rho _{1}g}{\rho h}\\ T=\frac{2\pi }{\sqrt{k}}\\ T=2\pi \sqrt{\frac{\rho h}{\rho_{1}g }}

Posted by

Sayak

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

PM Modi's Pariksha Pe Charcha 2025 to be held next month, registrations open till January 14
anam-khan

CBSE Board Exams 2025: Online portal for availing exemptions by CWSN students opens
anam-khan

Board Exams: States agree to equivalence; no question paper ‘jumbling’ from next year, says PARAKH CEO

Latest Question