INPhO — Indian National Physics Olympiad — Answer Writing
INPhO problems are long and multi-part, and the marks sit in the modelling: the right frame, the right conserved quantity, the right approximation. A candidate who sets the problem up correctly and slips in algebra outscores one who guesses a formula.
Answer all questions. State your assumptions and define every symbol you introduce. Marks are awarded for the setup as well as the final result.
- 1.A uniform solid cylinder of mass M and radius R rolls without slipping down an incline of angle θ. Find its acceleration and the minimum coefficient of friction required.12
- 2.Estimate the temperature at which the mean kinetic energy of a hydrogen molecule equals its gravitational binding energy at the Earth's surface.10
- 3.A charged particle enters a region of uniform magnetic field at an angle. Describe its trajectory quantitatively.14
One INPhO answer, from question to marked report
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A uniform solid cylinder of mass M and radius R rolls without slipping down an incline of angle theta. Find its acceleration and the minimum coefficient of friction required.
Type it, dictate it, or write on paper and photograph the page — your handwriting is read.
Photographed, read, and marked in red — every expected step scored down the right margin and the omissions written in.
For a rolling cylinder a = g sin(theta) / (1 + I/MR^2) = 2 g sin(theta) / 3 since I = MR^2/2. The friction force f = Ma/... and minimum coefficient of friction comes out as tan(theta)/3. Rolling without slipping means the point of contact is instantaneously at rest, so v = omega R and a = alpha R at every instant. The moment of inertia of a uniform solid cylinder about its axis is MR^2/2, and it is this factor which makes the acceleration two thirds of g sin(theta) instead of the full g sin(theta) that a block would have on a frictionless incline. Friction at the contact point does no work because that point does not move, so mechanical energy is conserved and the same acceleration can be obtained by the energy method as a check. The result is independent of M and R.
- A labelled free-body diagram before any algebra
- The two equations of motion written separately and the constraint that couples them
- The friction condition expressed as an inequality, not a value
Model answer for this question
Draw the free-body diagram with weight components, normal reaction and friction up the incline. Write Mg sin theta minus f equals Ma, and f R equals I alpha, with the rolling constraint a equals R alpha. Substitute I equals half MR squared and solve to a equals two thirds g sin theta. Back-substitute for f equals one third Mg sin theta, then impose f no greater than mu N to obtain mu at least one third tan theta, and state it as the condition for rolling without slipping.
Photograph the page from your phone and the Studio reads your handwriting — the only way to practise the speed and layout the paper actually tests.
Fast enough to write, read the report and rewrite the same answer in one sitting — which is where the improvement actually comes from.
The scoring behind those pen marks: every expected step, what it was worth, what you earned, and a model answer.
- Free-body diagram and forces identified0/2
No diagram. In a subjective physics paper the diagram is marked in its own right.
- Translational and rotational equations written separately1/3
The standard result is quoted rather than derived from the two equations.
- Rolling constraint stated1/2
Used implicitly; a equals R alpha should be written down.
- Acceleration obtained3/3
Correct.
- Friction condition derived to a clean inequality1/2
The final value is right but the working breaks off midway.
INPhO at a glance
| Conducting body | Homi Bhabha Centre for Science Education (HBCSE) |
|---|---|
| Mode | Handwritten solutions |
| Papers | 4 |
| Marking | INPhO — step marking |
What INPhO sets
The papers you sit, and what each is worth.
- Marked to the INPhO scheme
- Model answer, every time
- Handwriting read from a photo
- AI viva on any topic
- Full timed papers
- Every attempt kept in your archive
- WriteA question, answered and marked.
- VivaQuestioned on Rigid body rotation and more.
- Full paperA timed paper, one scorecard.