A simple pendulum oscillating in air has period T. The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is 161 th of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is

We know that, Time period of a pendulum is given byT=2πL/geffHere, L is the length of the pendulum and geff is the effective acceleration due to gravity in the respective medium in which bob is oscillating.Initially, when bob is oscillating in air, geff=g.So, initial time period, T=2πgLLet ρbob be the density of the bob.When this bob is dipped into a liquid whose density is given asρliquid=16ρbob=16ρ∴ Net force on the bob isFnet=Vρg−V⋅16ρ⋅g(where, V= volume of the bob = volume of displaced liquid by the bob when immersed in it). If the effective value of gravitational acceleration on the bob in this liquid is geff, then the net force on the bob can also be written asFnet=VρgeffEquating Eqs. (iii) and (iv), we haveVρgeff=Vρg−Vρg/16⇒geff=g−g/16=1615gthe new time period of the bob will beT′=2πgeffL=2π1516gL⇒T′=1516×2πgL=154×T

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Damped and forced oscillations

A simple pendulum oscillating in air has period T. The bob of

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A simple pendulum oscillating in air has period $T$ . The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is $\frac{1}{16}$ th of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is

2 T \frac{1}{10}

2 T \frac{1}{14}

4 T \frac{1}{14}

4 T \frac{1}{15}

Views: 5,525 students

Updated on: Oct 7, 2023

Book:

Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Exam:

JEE Mains 2019

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Emma Discussed

A simple pendulum oscillating in air has period

T

. The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is

\frac{1}{16}

th of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is

14 mins ago

Discuss this question LIVE

14 mins ago

Text solutionVerified

We know that, Time period of a pendulum is given by

T = 2 π L / g_{e ff}

Here,

L

is the length of the pendulum and

g_{e ff}

is the effective acceleration due to gravity in the respective medium in which bob is oscillating.
Initially, when bob is oscillating in air,

g_{e ff} = g

.
So, initial time period,

T = 2 π \frac{L}{g}

Let

ρ_{b o b}

be the density of the bob.
When this bob is dipped into a liquid whose density is given as

ρ_{l i q u i d} = \frac{ρ _{b o b}}{16} = \frac{ρ}{16}

∴

Net force on the bob is

F_{n e t} = V ρ g - V \cdot \frac{ρ}{16} \cdot g

(where,

V =

volume of the bob

=

volume of displaced liquid by the bob when immersed in it). If the effective value of gravitational acceleration on the bob in this liquid is

g_{e ff}

, then the net force on the bob can also be written as

F_{n e t} = V ρ g_{e ff}

Equating Eqs. (iii) and (iv), we have

V ρ g_{e ff} = V ρ g - V ρ g /16

\Rightarrow g_{e ff} = g - g /16 = \frac{15}{16} g

the new time period of the bob will be

T^{'} = 2 π \frac{L}{g _{e ff}} = 2 π \frac{16}{15} \frac{L}{g}

\Rightarrow T^{'} = \frac{16}{15} \times 2 π \frac{L}{g}

= \frac{4}{15} \times T

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Question Text	A simple pendulum oscillating in air has period $T$ . The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is $\frac{1}{16}$ th of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is
Updated On	Oct 7, 2023
Topic	Oscillations
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 11
Upvotes	980
Avg. Video Duration	5 min

A simple pendulum oscillating in air has period $T$ . The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is $\frac{1}{16}$ th of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is

Text solutionVerified

Filo tutor solutions (11)

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A simple pendulum oscillating in air has period T. The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is 161​ th of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is

Text solutionVerified

Filo tutor solutions (11)

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A simple pendulum oscillating in air has period $T$ . The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is $\frac{1}{16}$ th of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is