Question:
A pendulum bob has a speed of $3 \mathrm{~m} / \mathrm{s}$ at its lowest position. The pendulum is $50 \mathrm{~cm}$ long. The speed of bob, when the length makes an angle of $60^{\circ}$ to the vertical will be $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$_________ $\mathrm{m} / \mathrm{s}$.
Solution:
Applying work energy theorem :
$\mathrm{w}_{\mathrm{g}}+\mathrm{w}_{\mathrm{T}}=\Delta \mathrm{K}$
$-\mathrm{mgl}\left(1-\cos 60^{\circ}\right)=\frac{1}{2} \mathrm{mv}^{2}-\frac{1}{2} \mathrm{mu}^{2}$
$\mathrm{v}^{2}=\mathrm{u}^{2}-2 \mathrm{gl}\left(1-\cos 60^{\circ}\right)$
$\mathrm{v}^{2}=9-2 \times 10 \times 0.5\left(\frac{1}{2}\right)$
$\mathrm{v}^{2}=4$
$\mathrm{v}=2 \mathrm{~m} / \mathrm{s}$
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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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