Question:
The bob of a stationary pendulum is given a sharp hit to impart it a horizontal speed of $\sqrt{3} \mathrm{gl}$. Find the angle -rotated by the string before it becomes slack.
Solution:
$\frac{1}{2} \mathrm{~m} \mathrm{v}^{2}-\frac{1}{2} \mathrm{mu}^{2}=-\mathrm{mgh}$
$v^{2}=3 g l-2 g l(1+\cos \theta) \ldots \ldots \ldots 1$
and
$\left(m v^{2}\right) / l=m g \cos \theta$
$\mathrm{v}^{2}=\mathrm{gl} \cos \theta \ldots \ldots \ldots 2$
from equation 1 and 2
$3 g l-2 g l-2 g l \cos \theta=g l \cos \theta$
$\theta=\cos ^{-1}\left(\frac{1}{3}\right)$
Thus,
Angle $=180^{\circ}-\cos ^{-1}\left(\frac{\frac{1}{3}}{3}\right)$
Angle $=\cos ^{-1}(-1 / 3)$
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- 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
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- Atoms
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