Exploring Forces — NCERT Solutions

Given: A ball released from point P travels down an inclined plane and stops at point A on the horizontal surface due to friction.

Concept used: The force of friction depends on the nature (roughness) of the surfaces in contact. Greater roughness → greater friction → ball stops sooner. Lesser roughness → lesser friction → ball travels farther.

(i) To make the ball stop BEFORE point A:

We need to increase the force of friction on the ball so that it loses its speed faster and stops before reaching point A.

Method: Make the horizontal surface (and/or the inclined plane) rougher — for example, by spreading sand, placing a rough cloth (like a jute mat or sandpaper) on the surface between the bottom of the incline and point A. The increased friction will slow the ball down more quickly, and it will stop before point A.

(ii) To make the ball stop AFTER crossing point A:

We need to decrease the force of friction on the ball so that it retains its speed for longer and travels beyond point A.

Method: Make the horizontal surface smoother — for example, by polishing it, applying oil or wax, or placing a smooth glass sheet on the surface. The reduced friction will allow the ball to travel a greater distance and stop after crossing point A.

Conclusion: By increasing friction (rougher surface), the ball stops before A. By decreasing friction (smoother surface), the ball stops after A.

Given: People slip on smooth surfaces like ice or polished floors.

Concept used: Friction arises due to the irregularities (interlocking) between two surfaces in contact. The smoother the surface, the lesser the friction.

Explanation:

When we walk, we push the ground backward with our feet. The friction between our feet (or shoes) and the ground acts in the forward direction, which allows us to move forward without slipping. Friction thus provides the necessary grip.

On smooth surfaces like ice or polished floors, the surfaces are very smooth — they have very few irregularities. As a result, the interlocking between the surfaces of our feet/shoes and the floor is very poor, leading to very little friction.

Since the frictional force is very small, our feet cannot get a proper grip on the surface. When we try to push backward, the surface offers little resistance, and our feet slide, causing us to slip.

Conclusion: We slip on smooth surfaces because such surfaces have very little friction due to fewer surface irregularities, which reduces the grip between our feet and the surface.

Given: An object is in non-uniform motion (its speed is changing).

Concept used: A force is required to change the speed or direction of motion of an object. Non-uniform motion means the speed of the object is not constant — it is either increasing or decreasing.

Answer: Yes, a force is being applied to an object that is in non-uniform motion.

Explanation:

Non-uniform motion means the object's speed changes over time — it either speeds up (accelerates) or slows down (decelerates).

Since a force is needed to change the speed of an object, a net force must be acting on the object whenever it is in non-uniform motion.

Examples:

• A ball rolling on the ground slows down due to the force of friction (non-uniform motion).
• A ball thrown upward slows down due to gravitational force (non-uniform motion).
• A car speeding up has an engine force acting on it (non-uniform motion).

Conclusion: Yes, whenever an object is in non-uniform motion, a net force is acting on it, causing its speed to change.

Given: Weight of an object on the Moon $= \dfrac{1}{6}$ of its weight on the Earth.

Concept used:

• Weight is the force with which a planet/celestial body pulls an object towards itself. It depends on the gravitational force of that body.
• Mass is the amount of matter contained in an object. It does not depend on location.

What causes the change in weight?

The weight of an object depends on the gravitational force of the celestial body on which it is placed. The Moon is much smaller than the Earth and has much less mass. As a result, the gravitational force of the Moon is about one-sixth of the gravitational force of the Earth.

$$W_{\text{Moon}} = \frac{1}{6} \times W_{\text{Earth}}$$

Since weight = gravitational pull on the object, and the Moon's gravity is $\dfrac{1}{6}$th of Earth's gravity, the weight of the object on the Moon is one-sixth of its weight on the Earth.

Does the mass also become one-sixth?

No. The mass of the object does not change. Mass is the amount of matter in the object and remains the same everywhere — on Earth, on the Moon, or anywhere else in the universe. It is an intrinsic property of the object and does not depend on the gravitational force of the location.

$$m_{\text{Moon}} = m_{\text{Earth}}$$

Conclusion: The change in weight is caused by the weaker gravitational force of the Moon compared to the Earth. However, the mass of the object remains unchanged — it does not become one-sixth on the Moon.

Correct Option: (ii) $w_1 > w_2 > w_3$

Given: Three objects of the same size and shape but different materials are placed in water. They dip to different depths (from the figure, object 1 dips the deepest, object 2 dips to an intermediate depth, and object 3 dips the least / floats highest).

Concept used (Archimedes' Principle): When an object floats in a liquid, the buoyant force equals the weight of the object. The buoyant force equals the weight of the liquid displaced, which depends on the volume of the object submerged.

Reasoning:

Since all three objects are floating (not fully submerged), for each object:
$$\text{Weight of object} = \text{Buoyant force} = \text{Weight of water displaced}$$

The weight of water displaced depends on the volume of the object submerged (since all objects have the same shape and size, more depth submerged = more volume submerged = more water displaced = greater buoyant force needed = greater weight of object).

From Fig. 5.17 (as described): Object 1 dips deepest → displaces the most water → has the greatest weight. Object 3 dips the least → displaces the least water → has the smallest weight.

Therefore:
$$w_1 > w_2 > w_3$$

Answer: Option (ii) $w_1 > w_2 > w_3$