Q3:

Why is it advised to tie any luggage kept on the roof of a bus with a rope?

1. Theoretical Foundation: Newton’s First Law of Motion

The requirement to secure luggage to the roof of a moving vehicle is fundamentally grounded in Newton’s First Law of Motion, also known as the Law of Inertia. This law states that an object will remain at rest or continue to move at a constant velocity in a straight line unless acted upon by an external unbalanced force [Per Newton's First Law of Motion].

2. Analysis of Inertia in a Moving Vehicle

When luggage is placed on the roof of a bus, it possesses the same velocity as the bus. However, the luggage is not physically integrated into the structural frame of the vehicle. Its state of motion is governed by its own inertia—the tendency of an object to resist changes in its state of motion.

3. Diagrammatic Representation of Inertial Forces

4. Role of the Rope as an External Force

By tying the luggage with a rope, we introduce a tension force ($T$) that acts as the required external unbalanced force. This force effectively links the luggage to the bus frame. When the bus changes velocity or direction:

• The rope exerts a force that overcomes the luggage's inertia of motion/rest.
• The rope restricts the displacement of the luggage relative to the roof surface.
• Mathematically, the rope ensures that $F_{net}$ on the luggage remains zero relative to the vehicle, preventing displacement ($a = 0$ relative to the bus) [By Newton's Second Law: $F = ma$].

Final Solution: Luggage is tied to the roof of a bus because, according to Newton’s First Law, it possesses inertia of motion. If the bus accelerates, decelerates, or turns sharply, the luggage will attempt to maintain its state of motion, causing it to slide or fall. The rope provides the necessary external unbalanced force to tether the luggage to the bus, ensuring both move as a single system.