A metre scale is moving with uniform velocity. This implies (a) the force acting on the scale is zero, but a t

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Q. A metre scale is moving with uniform velocity. This implies

(a) the force acting on the scale is zero, but a torque about the centre of mass can act on the scale.

(b) the force acting on the scale is zero and the torque acting about centre of mass of the scale is also zero.

(d) neither the force nor the torque need to be zero.

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Concept understanding — Newton Second Law

Newton's Second Law: The Law That Connects Force and Motion

Imagine you're pushing a shopping cart. If you push gently, it moves slowly. Push harder, and it speeds up faster. Now imagine the cart is full of groceries — even with the same push, it accelerates much more slowly than an empty cart. This everyday experience is exactly what Newton's Second Law captures.

The Intuition First

Two things matter when you push something:

How hard you push — the force you apply.
How heavy the object is — its mass.

The harder you push, the more the object speeds up. The heavier the object, the less it speeds up for the same push. So acceleration depends on both force and mass — and in opposite ways.

Note

"Acceleration" here means any change in velocity — speeding up, slowing down, or changing direction. It's not just "going faster."

The Precise Statement

Newton's Second Law says:

The acceleration of an object is directly proportional to the net force acting on it, and inversely proportional to its mass. The acceleration is in the same direction as the net force.

In one equation:

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

Or more commonly:

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

Where:

$\vec{F}_{\text{net}}$ is the net force (the vector sum of all forces acting on the object) — measured in newtons (N)
$m$ is the mass of the object — measured in kilograms (kg)
$\vec{a}$ is the acceleration — measured in metres per second squared ( $\text{m/s}^2$ )

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

What This Really Means

Force causes acceleration, not velocity. A constant net force produces constant acceleration — meaning the velocity keeps changing at a steady rate. If you stop pushing, the net force becomes zero, and acceleration becomes zero (the object continues at constant velocity — that's Newton's First Law).

Mass is a measure of inertia. The more mass an object has, the harder it is to change its motion. A truck needs a much larger force than a bicycle to achieve the same acceleration.

Direction matters. Force and acceleration are vectors — they point the same way. If you push north, the acceleration is north. If multiple forces act, you must add them as vectors to find the net force.

A Simple Example

A 2 kg block is pushed with a net force of 10 N to the right.

a = \frac{F_{\text{net}}}{m} = \frac{10\ \text{N}}{2\ \text{kg}} = 5\ \text{m/s}^2

The block accelerates at $5\ \text{m/s}^2$ to the right. Every second, its velocity increases by 5 m/s in that direction.

Watch out

A common mistake: thinking that a constant force means constant velocity. It doesn't — constant force means constant acceleration, so velocity keeps changing. Only when net force is zero does velocity stay constant.

Why This Law Is So Powerful

Newton's Second Law is the bridge between forces (the causes) and motion (the effects). It lets you:

Predict how an object will move if you know the forces on it
Calculate the force needed to produce a desired motion
Understand why heavier things are harder to accelerate

It applies everywhere — from a ball you throw to a rocket launching into space. The same law governs them all.

For quick revision, remember that Newton Second Law is drawn directly from the Laws of Motion coverage of the NCERT/CBSE Class 11 Physics syllabus and recurs often in JEE Main and NEET papers, which is exactly why "Newton Second Law important questions" shows up so often in Physics question banks. The clearest way to build exam confidence here is to combine this explanation with the NCERT Physics textbook's own solved examples and chapter-end questions.

A metre scale moving with uniform velocity implies that both its linear and angular accelerations are zero. Consequently, the net force and the net torque acting on it must both be zero. The correct option is (B).

When a rigid body is described as "moving with uniform velocity," it means that its entire state of motion is constant. This includes both its translational motion (the motion of its center of mass) and its rotational motion (its rotation about its center of mass). Let's break this down using Newton's laws.

Understanding "Uniform Velocity" for Translational Motion: "Uniform velocity" means that the velocity vector $\vec{v}$ of the centre of mass of the scale is constant in both magnitude and direction. If the velocity is constant, then the linear acceleration $\vec{a}$ of the centre of mass must be zero:

\vec{a} = \frac{d\vec{v}}{dt} = 0

Relating Zero Acceleration to Net Force: According to Newton's Second Law of Motion for translational motion, the net external force ( $\Sigma \vec{F}$ ) acting on an object is equal to the product of its mass ( $m$ ) and its acceleration ( $\vec{a}$ ):

\Sigma \vec{F} = m\vec{a}

Since we established that $\vec{a} = 0$ for uniform velocity, it follows that:

\Sigma \vec{F} = m(0) = 0

Therefore, the net force acting on the scale is zero.

3. Understanding "Uniform Velocity" for Rotational Motion:

For a rigid body, "uniform velocity" also implies that its rotational state is constant. This means its angular velocity vector $\vec{\omega}$ (if it's rotating) is constant in both magnitude and direction. If the angular velocity is constant, then the angular acceleration $\vec{\alpha}$ must be zero:

\vec{\alpha} = \frac{d\vec{\omega}}{dt} = 0

If the scale were undergoing angular acceleration, its rotational motion would not be uniform, and the simple phrase "moving with uniform velocity" would be insufficient to describe its state.

4. Relating Zero Angular Acceleration to Net Torque:

According to Newton's Second Law of Motion for rotational motion, the net external torque ( $\Sigma \vec{\tau}$ ) acting on an object about its centre of mass is equal to the product of its moment of inertia ( $I$ ) about that axis and its angular acceleration ( $\vec{\alpha}$ ):

\Sigma \vec{\tau} = I\vec{\alpha}

Since we established that $\vec{\alpha} = 0$ for uniform velocity, it follows that:

\Sigma \vec{\tau} = I(0) = 0

Therefore, the net torque acting on the scale about its centre of mass is also zero.

> [!IMPORTANT]
> For a rigid body, "uniform velocity" implies both constant linear velocity (zero linear acceleration) and constant angular velocity (zero angular acceleration). This is a state of dynamic equilibrium.

Combining these two conclusions, both the net force and the net torque acting on the metre scale must be zero.

Let's evaluate the given options:

(A) the force acting on the scale is zero, but a torque about the centre of mass can act on the scale. (Incorrect, torque must also be zero)
(B) the force acting on the scale is zero and the torque acting about centre of mass of the scale is also zero. (Correct)
(C) the total force acting on it need not be zero but the torque on it is zero. (Incorrect, force must be zero)
(D) neither the force nor the torque need to be zero. (Incorrect, both must be zero)

✓Final answer

The correct option is (B), because uniform velocity implies both zero net force and zero net torque.

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Q.A metre scale is moving with uniform velocity. This implies