The blocks shown in figure have equal masses. The surface of $A$ is smooth but that of $B$ has a friction coefficient of $0.10$ with the floor. Block $A$ is moving at a speed of $10 \mathrm{~m} / \mathrm{s}$ towards $B$ which is kept at rest. Find the distance travelled by $B$ if (a) the collision is perfectly elastic and (b) the collision is perfectly inelastic. Take $g=10^{m} / \mathrm{s}^{2}$.
(a) Use C.O.L.M
$m_{A}(10)=m_{A} V_{1}+m_{B} V_{2} \quad\left\{m_{A}=m_{B}\right\}$
$V_{1}+V_{2}=10-(1)$
Use C.O.E.L,
Solving (1) and (2)
$10=\sqrt{100-V_{2}^{2}}+V_{2}$
$2 V_{2}^{2}-20 V_{2}=0 \Rightarrow V_{2}=(0,10) V_{1}=(10,0)$
If $V_{1}=0, V_{2}=10$
$m_{B} a_{B}=m_{B} \mu g=0.1 \times 10=1 \mathrm{~m} / \mathrm{s}^{2}$
Use kinematics law,
$v^{2}=u^{2}+2 a x$
$x=\frac{(10)^{2}}{2 \times 1}=50$
(b) If it is inelastic,
C.O.L.M $\Rightarrow m_{A}(10)=\left(m_{A}+m_{B}\right) V$
$m_{A}(10)=2 m V$
.$V=\frac{10}{2}=5 \mathrm{~m} / \mathrm{s}$
$2 m a_{B}=m \mu g \Rightarrow a_{B}=\frac{10}{2 \times 10}=0.5 \mathrm{~m} / \mathrm{s}^{2}$
$x=\frac{V^{2}}{2 a}=\frac{25}{2 \times \frac{1}{2}}=25$
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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,