A soap bubble of radius $3 \mathrm{~cm}$ is formed inside the another soap bubble of radius $6 \mathrm{~cm}$. The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is $\ldots \ldots . \mathrm{cm}$.
Excess pressure inside the smaller soap bubble
$\Delta \mathrm{P}=\frac{4 \mathrm{~S}}{\mathrm{r}_{1}}+\frac{4 \mathrm{~S}}{\mathrm{r}_{2}}$ .........(I)
The excess pressure inside the equivalent soap bubble
$\Delta \mathrm{P}=\frac{4 \mathrm{~S}}{\mathrm{R}_{\mathrm{eq}}} \ldots$ (ii)
From (i) \& (ii)
$\frac{4 \mathrm{~S}}{\mathrm{R}_{\mathrm{eq}}}=\frac{4 \mathrm{~S}}{\mathrm{r}_{1}}+\frac{4 \mathrm{~S}}{\mathrm{r}_{2}}$
$\frac{1}{\mathrm{R}_{\mathrm{eq}}}=\frac{1}{\mathrm{r}_{1}}+\frac{1}{\mathrm{r}_{2}}$
$=\frac{1}{6}+\frac{1}{3}$
$\mathrm{R}_{\mathrm{eq}}=2 \mathrm{~cm}$
Ans. $2.00$
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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,