INPhO 2025, Теория — Задача 1. The Flywheel Chronicles

Indian National Physics Olympiad (INPhO)-2025 — Question Paper · 2 февруари 2025 г. · 8 т.

Внимание: Бележка към темата

The complete retained original question and matching HBCSE solution packets are transcribed. The separately referenced Answer Booklet is not retained in the matching archive row. Printed key formula/sign/symbol/prose discrepancies and the original handwritten magnetic-data graph remain literal, with separately labelled source notes.

Original cover and instructions

Indian National Physics Olympiad (INPhO)-2025

HOMI BHABHA CENTRE FOR SCIENCE EDUCATION

Tata Institute of Fundamental Research

V. N. Purav Marg, Mankhurd, Mumbai, 400 088

Question Paper

Date: 02 February 2025

Time: 09:00-12:00 (3 hours)

Maximum Marks: 75

Instructions — Roll Number: □□□□−□□□□−□□□□\square\square\square\square-\square\square\square\square-\square\square\square\square

  1. This booklet consists of 9 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.
Question Number12345Total
Maximum Marks81416221575
Table of Constants
Speed of light in vacuumcc3.00×108 m⋅s−13.00\times10^8\ \mathrm{m\cdot s^{-1}}
Magnitude of electron chargeee1.60×10−19 C1.60\times10^{-19}\ \mathrm C
Value of 1/4πϵ01/4\pi\epsilon_09.00×109 N⋅m2⋅C−29.00\times10^9\ \mathrm{N\cdot m^2\cdot C^{-2}}
Avogadro’s numberNAN_A6.022×1023 mol−16.022\times10^{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\times10^{-23}\ \mathrm{J\cdot K^{-1}}
Permeability constantμ0\mu_04π×10−7 H⋅m−14\pi\times10^{-7}\ \mathrm{H\cdot m^{-1}}
Native key notice

The matching key repeats the cover, constant table, marks table and four instructions with “24 pages” and the title “Solutions”.

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

Условие

In the following experiment we are interested in determining the moment of inertia of a flywheel. The free ends of the axle in a flywheel assembly are placed inside grooves at both ends, to rigid supports provided on the wall (see diagram below). The diameter of the axle is d=2.72 cmd=2.72\ \mathrm{cm}. The total work done by the axle in overcoming the friction in the two grooves per rotation is WW. A massless string, attached to a point mass mm is wound tightly in nn turns (without overlap) on the axle. The string unwinds from the axle without slipping as the mass descends from an initial height hh. The length of the string is adjusted such that when the mass just touches the floor, the string detaches from the axle.

Full native flywheel/axle/string/mass/two rigid supports/diameter d/height h/floor geometry.

From the instant when the mass touches the floor (taken as t=0t=0), the flywheel continues to rotate, adding another NN number of rotations before coming to rest in time t=Tt=T. The figure is not to scale.

a) Derive an expression for the moment of inertia II of the flywheel in terms of m,N,Tm,N,T, and other known parameters. [5 т.]

b) The following data has been obtained in this experiment.

mm (gm)NNTT (sec)
150.0145.25190.0
200.0200.00225.5
250.0238.50235.5

Calculate the value of II for n=16n=16, and h=139 cmh=139\ \mathrm{cm}. [3 т.]

Решение

Native source end

END OF THE QUESTION PAPER

The key also ends with this native wording on page24. Key page20 is blank apart from running page and roll-number furniture.

Оригинал в Архива: INPhO2025-Question.pdf · официални решения: INPhO2025-Solution-20250219.pdf