Two small balls $A$ and $B$, each of mass $m$, are joined rigidly by a light horizontal rod of length $L$. The system translates on a frictionless horizontal surface with a velocity $v_{0}$ in a direction perpendicular to the rod. A particle $P$ of mass $m$ kept at rest on the surface sticks to the ball $A$ as the ball collides with it. Find
(a) the linear speeds of the balls $A$ and B after the collision, (b) the velocity of the centre of mass $C$ of the system $A+B+P$ and (c) the system about $C$ after the collision.
[Hint: The light rod will exert a force on the ball B only along its length.]
(a) The light rod will exert a force on the ball B only along its length. So collision will not effect its velocity.
$v_{B}=v_{O}$
Momentum conservation for ball $A$
$m^{v_{O}}=2 m^{v_{A}}$
$v_{A}=\frac{v_{0}}{2}$
(b)
$\overrightarrow{v_{C M}}=\frac{m_{1} \overrightarrow{v_{1}}+m_{2} \overrightarrow{v_{2}}}{m_{1}+m_{2}}$
$=\frac{m w 0+2 m\left(\frac{\mathrm{mO}}{\mathrm{n}}\right)}{m+2 m}$
$\overrightarrow{v_{C M}}=\frac{2 v_{0}}{3}$
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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,