In which of the following examples of motion, can the body be considered approximately a point object: (a) a r

Exercises · 2.1

Q. In which of the following examples of motion, can the body be considered approximately a point object:

(a) a railway carriage moving without jerks between two stations.

(b) a monkey sitting on top of a man cycling smoothly on a circular track.

(d) a tumbling beaker that has slipped off the edge of a table.

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Concept understanding — Point Object Approximation

Point Object Approximation — The First Encounter

Imagine you're looking at a bus moving on a road. If someone asks you "where is the bus right now?", you'd probably point to a spot on the road and say "it's near that tree." You don't care about the bus's length, its shape, or which part of the bus is exactly at the tree — you treat the whole bus as if it were a single dot at that location.

That's the core intuition behind the point object approximation: when the size and internal structure of an object don't matter for the problem you're solving, you can replace the entire object with a single point — usually its centre of mass — and analyse its motion as if all its mass were concentrated there.

When does this approximation work?

The approximation is valid when the size of the object is negligible compared to the distances involved in the problem. More precisely:

\frac{\text{size of object}}{\text{distance travelled or distance from reference}} \ll 1

If this ratio is very small (say, less than 0.01), the object's shape and orientation won't affect the answer significantly.

Examples where it works:

A cricket ball thrown from one end of a field to the other — the ball's diameter (~7 cm) is tiny compared to the 70 m throw.
Earth orbiting the Sun — Earth's radius (~6400 km) is negligible compared to the 150 million km distance to the Sun.
A car moving from Delhi to Agra — the car's length (~4 m) is insignificant compared to the 200 km journey.

Examples where it fails:

A rotating fan blade — you cannot treat it as a point because different parts move at different speeds.
A person walking — if you're studying their gait, the shape matters.
A train entering a tunnel — the train's length is comparable to the tunnel's length, so you cannot ignore it.

The precise statement

Important

An object can be treated as a point object (or a particle) if, during the entire motion under consideration, its size and internal structure are irrelevant to the description of its motion. In such cases, the object's translational motion is fully described by the motion of a single point — typically its centre of mass.

This means:

You ignore rotation, vibration, or any deformation of the object.
You only care about the path traced by that one point.
All forces acting on the object are assumed to act at that single point.

A common misconception

Watch out

Many students think "small object = point object". That's not always true. A tiny grain of sand is small, but if you're studying how it tumbles in a fluid, its shape matters — so it's not a point object. Conversely, a huge planet can be a point object if you're only interested in its orbit around the Sun.

The key is relevance, not size alone.

Why do we use it?

Physics becomes dramatically simpler. Instead of tracking every atom in a bus, you write one equation:

\vec{F}_{\text{net}} = m \vec{a}

where $m$ is the total mass and $\vec{a}$ is the acceleration of the centre of mass. That's the power of the approximation — it reduces a complex extended body to a single mathematical point, letting you focus on the big picture of motion.

Quick check for yourself

A 2 m long rod is sliding on a frictionless table. Can you treat it as a point object if:

You want to find how long it takes to travel 10 m? → Yes (size << distance)
You want to find how fast its ends are moving? → No (rotation matters)

The first time you meet this idea, remember: when the object's size is irrelevant to the question, shrink it to a point and move on.

Point Object Approximation is introduced at the very start of the NCERT Class 11 Physics chapter on Motion in a Straight Line, matching searches like "point object: definition physics" or "kinematics important questions class 11 physics". Understanding when an object's size can be ignored is foundational groundwork for every later mechanics topic tested in CBSE boards and is an important topic for JEE Main and NEET as well.

A body can be treated as a point object when its size is negligible compared to the scale of the motion being described, and its internal/rotational motion doesn't matter to the problem. Both the railway carriage (a) and the monkey-on-cyclist (b) satisfy this; the spinning cricket ball (c) and the tumbling beaker (d) do not, since their rotation is exactly what the problem describes.

The Point-Object Test

A body is (approximately) a point object when:

Its own size is much smaller than the distance/scale over which its motion is being studied, and
Its internal structure, shape, or rotation is not relevant to the question being asked.

Applying this to each case:

(a) Railway carriage moving without jerks between stations

A carriage is a few tens of metres long; the distance between two stations is several kilometres. The carriage's length is negligible compared to this distance, and "moving without jerks" means we only care about its overall straight-line translation, not its shape or any internal motion.

Point object: YES.

(b) Monkey sitting on top of a man cycling on a circular track

The man-monkey system is a couple of metres tall, while the track itself has a radius/circumference many times larger — typically tens of metres or more for a circular cycling track. Since we are only interested in the smooth motion of the man+monkey around the track (not the monkey's posture, balance, or motion relative to the man), the combined size is negligible compared to the scale of the track, and no rotational/internal detail matters to describing that motion.

Point object: YES.

(c) Spinning cricket ball that turns sharply on hitting the ground

Here the whole point of the question is the ball's spin and how it makes the ball turn sharply — this is a rotational effect that depends directly on the ball's finite size and its contact with the ground. You cannot answer "why does it turn?" while treating the ball as having no size or rotation.

Point object: NO.

(d) Tumbling beaker that has slipped off a table

"Tumbling" is explicitly a description of rotational motion — the beaker's orientation keeps changing as it falls. Capturing this needs the beaker's shape, extent, and moment of inertia; a point has none of these.

Point object: NO.

Conclusion

Both (a) and (b) describe motions where the body's size is negligible on the relevant scale and where rotation/internal structure is irrelevant to the question asked, so both qualify as (approximately) point objects. (c) and (d) are explicitly about rotational behaviour, so they do not.

✓Final answer

The body can be considered approximately a point object in (a) and (b) .

Concept: The Point-Object Idealisation as a Counterfactual Test

Method: The "Could a Point Do This?" Thought Experiment

Rather than checking two separate conditions (small relative size, and whether rotation matters) as a checklist, this method asks one sharper question for each case: if the body were shrunk to a mathematical point — zero size, no orientation, no spin — could the described phenomenon still happen at all? If yes, the point-object idealisation is safe; if the phenomenon is itself defined by the body's finite size or rotation, a point cannot reproduce it, and the idealisation fails.

Steps — apply the test to each case

(a) Railway carriage moving without jerks between stations. The question only concerns the carriage's overall position along the track over a distance of kilometres. A point moving along the same track traces exactly the same journey — nothing about "moving without jerks" requires the carriage to have any length or shape.

→ Point idealisation valid.
(b) Monkey on a cyclist moving smoothly around a circular track. The question only concerns the man+monkey system's path around the track (radius far larger than their combined size). A point moving along that same circular path reproduces the described motion completely — the monkey's balance or posture is never asked about.

→ Point idealisation valid.
(c) A spinning cricket ball that turns sharply on hitting the ground. Here the very phenomenon being described — the sideways turn upon impact — is caused by the ball's spin, which requires the ball to have a surface making contact with the ground and rotating about its own axis. A point has no surface and no axis to spin about; shrink the ball to a point and the "turning sharply" effect vanishes entirely, because the physics being asked about is the finite-size/rotation effect.

→ Point idealisation fails.
(d) A tumbling beaker that has slipped off a table. "Tumbling" means the beaker's orientation is continuously changing as it falls — that is literally a statement about its finite shape and rotation. A point object has no orientation to tumble.

→ Point idealisation fails.

Why this test is sharper than a checklist

A scale-only check (comparing sizes) can mislead if applied carelessly — a cricket ball is also "small" compared to the pitch, the same way a carriage is small compared to the distance between stations. The counterfactual question cuts straight to what actually matters: is the described behaviour itself a consequence of finite size/rotation, regardless of how small the object is on some other scale?

Final Answer

The body can be treated as a point object in $\boxed{\text{(a) and (b)}}$ ; not in (c) or (d), because the very motion described there — spin-induced turning, and tumbling — cannot occur for an object with no size or orientation.

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Q.In which of the following examples of motion, can the body be considered approximately a point object: