Question:
A particle of mass $\mathrm{m}$ is suspended from a ceiling through a string of length $L$. The particle moves in
a horizontal circle of radius $r$ such that $r=\frac{L}{\sqrt{2}}$. The
speed of particle will be :
$\sqrt{1 g}$
$\sqrt{2 \mathrm{rg}}$
$2 \sqrt{\mathrm{rg}}$
$\sqrt{\frac{\mathrm{rg}}{2}}$
Correct Option: 1
Solution:
$\mathrm{r}=\frac{\ell}{\sqrt{2}}$
$\sin \theta=\frac{\mathrm{r}}{\ell}=\frac{1}{\sqrt{2}}$
$\theta=45^{\circ}$
$T \sin \theta=\frac{m v^{2}}{r}$
$\mathrm{T} \cos \theta=\mathrm{mg}$
$\tan \theta=\frac{v^{2}}{r g} \Rightarrow v=\sqrt{r g}$
Ans. 1
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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,
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