NCERT solution Class 11 oscillations

NCERT Solutions

Class 11 Physics

Oscillations

NCERT Questions

Q. 13.1
Q. 13.2
Q. 13.3
Q. 13.4
Q. 13.5
Q. 13.6
Q. 13.7
Q. 13.8
Q. 13.9
Q. 13.10
Q. 13.11
Q. 13.12
Q. 13.13
Q. 13.14
Q. 13.15
Q. 13.16
Q. 13.17
Q. 13.18
Q. 14.7
Q. 14.8

Q. 13.17

A cylindrical piece of cork of density of base area A and height h floats in a liquid of density ρl. The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period

T= 2π √ (hρ_l) / (gρ_l) where ρ is the density of cork. (Ignore damping due to viscosity of the liquid).

Base area of the cork = A

Height of the cork = h

Density of the liquid = ρ1

Density of the cork = ρ

In equilibrium:

Weight of the cork = Weight of the liquid displaced by the floating cork

Let the cork be depressed slightly by x. As a result, some extra water of a certain volume is displaced. Hence, an extra up-thrust acts upward and provides the restoring force to the cork.

Up-thrust = Restoring force, F = Weight of the extra water displaced

F = – (Volume × Density × g)

Volume = (Area × Distance through which the cork is depressed)

Volume = Ax

∴ F = – (A x ρ1 g)..... (i)

According to the force law:

F = kx

k = (F/x) where, k is constant

k = (F/x)

= - (Aρ1 g).... (ii)

The time period of the oscillations of the cork:

T = 2π√ (m/k) .... (iii)

Where,

m = Mass of the cork

= (Volume of the cork × Density)

= (Base area of the cork × Height of the cork × Density of the cork) = (Ahρ)

Hence, the expression for the time period becomes:

T=2π√ (Ahρ)/ (Ahρ1g)

T = 2π√ (hρ)/ (ρ1g)

Video solution:

Oscillations Class 11 Physics NCERT Chapter 13 NCERT Solutions

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NCERT solutions of Oscillations Class 11 Physics - all questions of all exercises are solved. Q. No. 1, 2, 3, and so on. Complete explanation and detailed solution makes them the best videos for Class 11 Physics Oscillations NCERT solutions.