A dumb-bell consists of two identical small balls of mass $1 / 2 \mathrm{~kg}$ each connected to the two ends of a $50 \mathrm{~cm}$ long light rod. The dumb-bell is rotating about a fixed axis through the centre of the rod and perpendicular to it at an angular speed of $10 \mathrm{rad} / \mathrm{s}$. An impulsive force of average magnitude $5.0 \mathrm{~N}$ acts on one of the masses in the direction of its velocity for $0.10 \mathrm{~s}$. Find the new angular velocity of the system.
$\mathrm{T}=\mathrm{I \omega}$
$\mathrm{F} \times \mathrm{r}=\left(m r^{2}+m r^{2}\right) \alpha$
$5(0.25)=2\left(\frac{1}{2}\right)(0.5)^{2} \alpha$
$\alpha=20 \mathrm{rad} / \mathrm{s}^{2}$
$\omega_{0}=10 \mathrm{rad} / \mathrm{sec}$
$\mathrm{T}=0.1$
$\omega=\omega_{0}+\alpha_{\mathrm{T}}$
$\omega=12 \mathrm{rad} / \mathrm{sec}$
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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,