A ball is travelling with uniform translatory motion. This means that (a) it is at rest. (b) the path can be a straight line or circular and the ball travels with uniform speed. (c) all parts of the ball have the same velocity (magnitude and direction) and the velocity is constant. (d) the centre of the ball moves with constant velocity and the ball spins about its centre uniformly.

A ball is travelling with uniform translatory motion. This means that (a) it is at rest. (b) the path can be a

NCERT Exemplar · Q1

Q. A ball is travelling with uniform translatory motion. This means that

(a) it is at rest.

(b) the path can be a straight line or circular and the ball travels with uniform speed.

(d) the centre of the ball moves with constant velocity and the ball spins about its centre uniformly.

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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.

Uniform translatory motion means every particle of the body has the same velocity vector at every instant — the body moves without rotation, and the velocity is constant in both magnitude and direction. The correct option is (C).

The Concept: What "Uniform Translatory Motion" Really Means

When we say a ball is in translatory motion, we mean the entire object moves as one piece — every point in the ball follows a parallel path. Think of a box sliding across a frictionless floor without tipping: the top, bottom, left, and right all move exactly the same way. That's translation.

Now add "uniform" to it. Uniform motion means constant velocity — no change in speed and no change in direction. So uniform translatory motion is the simplest kind of motion: every particle of the object has the same velocity vector, and that vector never changes.

Watch out

A common mistake is to confuse "uniform speed" with "uniform velocity." Uniform speed means the magnitude is constant, but the direction could still change (as in circular motion). Uniform velocity means both magnitude and direction are constant — that's a stricter condition.

Step-by-Step Analysis

1. What does translatory motion imply?

In pure translation, every particle of the body undergoes identical displacement in the same time interval. This means all parts have the same velocity vector at any given instant. There is no rotation — the ball does not spin about its centre. If it spun, different points would have different velocities (some moving faster, some slower, some in opposite directions), which violates the definition of translation.

2. What does uniform motion imply?

Uniform motion means constant velocity — zero acceleration. The velocity vector does not change with time. So the speed is constant and the direction is constant. This forces the path to be a straight line. A circular path, even at constant speed, involves a changing direction (centripetal acceleration), so it is not uniform motion.

3. Putting it together: uniform translatory motion

Every particle of the ball has the same velocity vector, and that vector is constant in time. The ball moves in a straight line at constant speed, without rotating. The centre of the ball moves with constant velocity, and because there is no rotation, every other point also moves with that same constant velocity.

4. Evaluating the options

(A) it is at rest. Rest is a special case of uniform translatory motion (velocity = 0), but uniform translatory motion does not require rest. So this is too narrow.
(B) the path can be a straight line or circular and the ball travels with uniform speed. Circular motion at uniform speed is not uniform motion because the velocity direction changes. Also, translatory motion in a circle would require the ball to rotate (like a car going around a curve), which is not pure translation. This option is wrong on two counts.
(C) all parts of the ball have the same velocity (magnitude and direction) and the velocity is constant. This is exactly the definition we built. Every part shares the same velocity vector, and that vector does not change. Correct.
(D) the centre of the ball moves with constant velocity and the ball spins about its centre uniformly. Spinning means different parts have different velocities — that's rotation, not translation. So this contradicts the definition of translatory motion.

Tip

A quick way to test option (D): imagine a spinning ball on a frictionless surface. Its centre might move with constant velocity, but a point on the rim moves in loops relative to the ground. That point's velocity changes direction constantly — not uniform motion for the ball as a whole.

✓Final answer

The correct option is (C) .

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Q.A ball is travelling with uniform translatory motion. This means that

Concept understanding — Point Object Approximation

Point Object Approximation — The First Encounter

When does this approximation work?

The precise statement

A common misconception

Why do we use it?

Quick check for yourself

The Concept: What "Uniform Translatory Motion" Really Means

Step-by-Step Analysis

Concept: Definition of Uniform Translatory Motion

Q.A ball is travelling with uniform translatory motion. This means that

The Concept: What "Uniform Translatory Motion" Really Means

Step-by-Step Analysis

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