During a heavy rain, hailstones of average size $1.0 \mathrm{~cm}$ in diameter fall with an average speed of $20 \mathrm{~m} / \mathrm{s}$. Suppose 2000 hailstorms strike every square meter of a $10 \mathrm{~m}^{\times} 10 \mathrm{~m}$ roof perpendicularly in one second and the average force exerted by the falling hailstones on the roof. Density of a hailstone is $900^{\mathrm{kg} / \mathrm{m}^{3}}$
Volume of 1 hailstorm
$=\frac{4}{3} \pi\left(\frac{10^{-2}}{2}\right)^{3}=\frac{4}{24} \pi \times 10^{-6}$
$=\frac{\pi}{6} \times 10^{-6} \mathrm{~m}^{3}$
Mass $=\rho . V=9000 \times \frac{\pi}{6} \times 10^{-6}$
$=150 \pi \times 10^{-6} \mathrm{~kg}$
Mass of 2000 hailstorms $=2000 \times 150 \pi \times 10^{-6}$
$=0.3 \pi_{\mathrm{kg}}$
average force on $1^{m^{3}}$ roof
$=\frac{\Delta p}{\Delta t} \frac{d p}{d t}=\frac{0.3 \pi \times 20}{1}=18.84 \sim 19$
Average force on $10 \mathrm{~m} \times 10 \mathrm{~m}\left(100^{\mathrm{m}^{2}}\right)$ roof
$=19 \times 100=1900 \mathrm{~N}$
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- 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
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