A large block of wood of mass $\mathrm{M}=5.99 \mathrm{~kg}$ is hanging from two long massless cords. A bullet of mass $m=10 \mathrm{~g}$ is fired into the block and gets embedded in it. The (block + bullet) then swing upwards, their centre of mass rising a vertical distance $\mathrm{h}=9.8 \mathrm{~cm}$ before the (block + bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before collision is : (Take $\mathrm{g}=9.8 \mathrm{~ms}^{-2}$ )
$841.4 \mathrm{~m} / \mathrm{s}$
$811.4 \mathrm{~m} / \mathrm{s}$
$831.4 \mathrm{~m} / \mathrm{s}$
$821.4 \mathrm{~m} / \mathrm{s}$
Correct Option: , 3
From energy conservation,
$\left[\begin{array}{l}\text { after bullet gets embedded till the } \\ \text { system comes momentarily at rest }\end{array}\right]$
$(\mathrm{M}+\mathrm{m}) \mathrm{g} h=\frac{1}{2}(\mathrm{M}+\mathrm{m}) \mathrm{v}_{1}^{2}$
[ $\mathrm{v}_{1}$ is velocity after collision]
$\therefore v_{1}=\sqrt{2 g h}$
Applying momentum conservation, (just before and just after collision)
$\mathrm{mv}=(\mathrm{M}+\mathrm{m}) \mathrm{v}_{1}$
$v=\left(\frac{\mathrm{M}+\mathrm{m}}{\mathrm{m}}\right) \mathrm{v}_{1}=\frac{6}{10 \times 10^{-3}} \times \sqrt{2 \times 9.8 \times 9.8 \times 10^{-2}}$
$\approx 831.55 \mathrm{~m} / \mathrm{s}$
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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,