A bob of mass ' $m$ ' suspended by a thread of length $l$ undergoes simple harmonic oscillations with time period T. If the bob is immersed in a liquid that has density $\frac{1}{4}$ times that of the bob and the length of
the thread is increased by $1 / 3^{\text {rd }}$ of the original length, then the time period of the simple harmonic oscillations will be :-
$\mathrm{T}$
$\frac{3}{2} \mathrm{~T}$
$\frac{3}{4} T$
$\frac{4}{3} T$
Correct Option: , 4
$\mathrm{T}=2 \pi \sqrt{\ell / \mathrm{g}}$
When bob is immersed in liquid $\mathrm{mg}_{\text {eff }}=\mathrm{mg}-$ Buoyant force
$\mathrm{mg}_{\text {eff }}=\mathrm{mg}-\mathrm{v} \sigma \mathrm{g}$ $(\sigma=$ density of liquid $)$
$=m g-V \frac{\rho}{4} g$
$=\mathrm{mg}-\frac{\mathrm{mg}}{4}=\frac{3 \mathrm{mg}}{4}$
$\therefore \mathrm{g}_{\text {eff }}=\frac{3 \mathrm{~g}}{4}$
$\mathrm{T}_{1}=2 \pi \sqrt{\frac{\ell_{1}}{\mathrm{~g}_{\mathrm{eff}}}} \quad \ell_{1}=\ell+\frac{\ell}{3}=\frac{4 \ell}{3}, \quad \ell_{\mathrm{eff}}=\frac{3 \mathrm{~g}}{4}$
By solving
$\mathrm{T}_{1}=\frac{4}{3} 2 \pi \sqrt{\ell / \mathrm{g}}$
$\mathrm{T}_{1}=\frac{4 \mathrm{~T}}{3}$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,