INPhO 2023, Теория — Задача 1. Dancing on the floor

Indian National Physics Olympiad (INPhO)-2023 — Question Paper · 29 януари 2023 г. · 6 т.

Указания

Date: 29 January 2023

Time: 09:00-12:00 (3 hours) Maximum Marks: 60

Instructions Roll No.:

  1. This booklet consists of 6 pages and total of 5 questions. Write roll number at the top wherever asked.
  2. Booklet to write the answers is provided separately. Instructions to write the answers are on the Answer Booklet.
  3. Non-programmable scientific calculators are allowed. Mobile phones cannot be used as calculators.
  4. Please submit the Answer Sheet at the end of the examination. You may retain the Question Paper.

Table of Constants

Speed of light in vacuumcc3.00×108 m⋅s−13.00 \times 10^{8}\ \mathrm{m{\cdot}s^{-1}}
Planck’s constanthh6.63×10−34 J⋅s6.63 \times 10^{-34}\ \mathrm{J{\cdot}s}
ℏ\hbarh/2πh/2\pi
Universal constant of GravitationGG6.67×10−11 N⋅m2⋅kg−26.67 \times 10^{-11}\ \mathrm{N{\cdot}m^2{\cdot}kg^{-2}}
Magnitude of electron chargeee1.60×10−19 C1.60 \times 10^{-19}\ \mathrm{C}
Rest mass of electronmem_e9.11×10−31 kg9.11 \times 10^{-31}\ \mathrm{kg}
Value of 1/4πϵ01/4\pi\epsilon_09.00×109 N⋅m2⋅C−29.00 \times 10^{9}\ \mathrm{N{\cdot}m^2{\cdot}C^{-2}}
Avogadro’s numberNAN_A6.022×1023 mol−16.022 \times 10^{23}\ \mathrm{mol^{-1}}
Acceleration due to gravitygg9.81 m⋅s−29.81\ \mathrm{m{\cdot}s^{-2}}
Universal Gas ConstantRR8.31 J⋅K−1⋅mol−18.31\ \mathrm{J{\cdot}K^{-1}{\cdot}mol^{-1}}
RR0.0821 l⋅atm⋅mol−1⋅K−10.0821\ \mathrm{l{\cdot}atm{\cdot}mol^{-1}{\cdot}K^{-1}}
Boltzmann constantKBK_B1.3806×10−23 J⋅K−11.3806 \times 10^{-23}\ \mathrm{J{\cdot}K^{-1}}
Permeability constantμ0\mu_04π×10−7 H⋅m−14\pi \times 10^{-7}\ \mathrm{H{\cdot}m^{-1}}
1 Angstrom unit1Å1×10−10 m1 \times 10^{-10}\ \mathrm{m}
1 micro unit1μ1\mu1×10−61 \times 10^{-6} units
1 electron volt1 eV1.6×10−19 J1.6 \times 10^{-19}\ \mathrm{J}
Q No12345Total
Maximum Marks6616161660
Указания

Date: 29 January 2023

Time: 09:00-12:00 (3 hours) Maximum Marks: 60

Instructions Roll No.:

  1. This booklet consists of 19 pages and total of 5 questions. Write roll number at the top wherever asked.
  2. Booklet to write the answers is provided separately. Instructions to write the answers are on the Answer Booklet.
  3. Non-programmable scientific calculators are allowed. Mobile phones cannot be used as calculators.
  4. Please submit the Answer Sheet at the end of the examination. You may retain the Question Paper.

Table of Constants

Speed of light in vacuumcc3.00×108 m⋅s−13.00 \times 10^{8}\ \mathrm{m{\cdot}s^{-1}}
Planck’s constanthh6.63×10−34 J⋅s6.63 \times 10^{-34}\ \mathrm{J{\cdot}s}
ℏ\hbarh/2πh/2\pi
Universal constant of GravitationGG6.67×10−11 N⋅m2⋅kg−26.67 \times 10^{-11}\ \mathrm{N{\cdot}m^2{\cdot}kg^{-2}}
Magnitude of electron chargeee1.60×10−19 C1.60 \times 10^{-19}\ \mathrm{C}
Rest mass of electronmem_e9.11×10−31 kg9.11 \times 10^{-31}\ \mathrm{kg}
Value of 1/4πϵ01/4\pi\epsilon_09.00×109 N⋅m2⋅C−29.00 \times 10^{9}\ \mathrm{N{\cdot}m^2{\cdot}C^{-2}}
Avogadro’s numberNAN_A6.022×1023 mol−16.022 \times 10^{23}\ \mathrm{mol^{-1}}
Acceleration due to gravitygg9.81 m⋅s−29.81\ \mathrm{m{\cdot}s^{-2}}
Universal Gas ConstantRR8.31 J⋅K−1⋅mol−18.31\ \mathrm{J{\cdot}K^{-1}{\cdot}mol^{-1}}
RR0.0821 l⋅atm⋅mol−1⋅K−10.0821\ \mathrm{l{\cdot}atm{\cdot}mol^{-1}{\cdot}K^{-1}}
Boltzmann constantKBK_B1.3806×10−23 J⋅K−11.3806 \times 10^{-23}\ \mathrm{J{\cdot}K^{-1}}
Permeability constantμ0\mu_04π×10−7 H⋅m−14\pi \times 10^{-7}\ \mathrm{H{\cdot}m^{-1}}
1 Angstrom unit1Å1×10−10 m1 \times 10^{-10}\ \mathrm{m}
1 micro unit1μ1\mu1×10−61 \times 10^{-6} units
1 electron volt1 eV1.6×10−19 J1.6 \times 10^{-19}\ \mathrm{J}
Q No12345Total
Maximum Marks6616161660

Please note that alternate/equivalent methods and different way of expressing final solutions may exist. A correct method will be suitably awarded.

Условие

There are various apps that record the intensity of an audio signal. An app (WaveEditorTM^{\mathrm{TM}} here) displays the audio signal as a wave, whose amplitude is proportional to the audio signal’s loudness. A smartphone with this app recording the sound signal is kept on a uniformly built flat floor of a classroom.

Screenshot of an audio waveform recording: a grey noisy band with sharp vertical spikes at the bounces, labelled with timestamps 10.260, 11.409, 12.244, 12.848, 13.284, 13.602, 13.832 and 14.000; further unlabelled spikes crowd together to the right.

A perfectly small spherical steel ball is thrown up such that it almost touches the ceiling and comes back without hitting. The ball hits the floor and thereafter it keeps bouncing. The app records the sound signal produced when the ball hits the floor on every bounce. A screenshot of the recording is shown. The timestamps (in seconds) of the first eight consecutive bounces are also shown next to the peak. For example, the app records a peak at 10.260 s when the first time the ball hits the floor.

Make reasonable assumptions, when the ball hits the floor and calculate the height of the classroom from the given data. State your assumptions clearly.

Отговори

Решение

Оригинал в Архива: INPhO2023-Question.pdf · официални решения: INPhO2023-Solution-20230215.pdf