How Forces Affect Motion (Force & Laws of Motion): NCERT Solutions (2026)

Inertia is a measure of the mass of an object. The heavier the object, the greater its inertia.

• (a) A stone has more inertia than a rubber ball of the same size because it has more mass.
• (b) A train has much more mass than a bicycle, so the train has more inertia.
• (c) A five-rupee coin has more mass than a one-rupee coin, so it has more inertia.

The velocity of the football changes four times:

1. First time: When the first player kicks the ball. (Agent: First player's foot).
2. Second time: When the second player kicks the ball towards the goal. (Agent: Second player's foot).
3. Third time: When the goalkeeper collects (stops) the football. (Agent: Goalkeeper's hands).
4. Fourth time: When the goalkeeper kicks the ball to his teammate. (Agent: Goalkeeper's foot).

This happens due to the Inertia of Rest. When we vigorously shake the branch, the branch comes into motion. However, the leaves tend to remain in their state of rest due to inertia. This relative motion between the moving branch and the resting leaves causes a strain, and the weakly attached leaves get detached and fall down.

• Falling forward: When a moving bus brakes suddenly, the lower part of our body comes to rest along with the bus. But the upper part of our body continues to move forward due to the Inertia of Motion, causing us to fall forward.
• Falling backward: When a bus accelerates from rest, the lower part of our body moves forward with the bus, but the upper part tries to remain at rest due to the Inertia of Rest, causing us to fall backward.

According to Newton's Third Law, action and reaction are equal and opposite, but they act on two different bodies.

When the horse pushes the ground backwards with its feet (Action), the ground pushes the horse forward with an equal and opposite force (Reaction). It is this forward reaction force of the ground on the horse that allows the horse to move forward, pulling the cart along with it.

This is an application of Newton's Third Law and conservation of momentum. When a large amount of water is ejected from a hose at a high velocity in the forward direction (Action), the water exerts an equal and opposite backward force on the hose (Reaction). This strong backward push makes it difficult for the fireman to hold the hose steady.

Given:
Mass of rifle ($m_1$) = 4 kg
Mass of bullet ($m_2$) = 50 g = 0.05 kg (always convert grams to kg!)
Initial velocity of both rifle and bullet before firing is zero ($u_1 = 0$, $u_2 = 0$).
Final velocity of bullet ($v_2$) = 35 m/s
Final recoil velocity of rifle ($v_1$) = ?

Using the Law of Conservation of Momentum:
Total momentum before firing = Total momentum after firing
$$m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$$
$$0 = (4 \times v_1) + (0.05 \times 35)$$
$$0 = 4v_1 + 1.75$$
$$4v_1 = -1.75$$
$$v_1 = \frac{-1.75}{4}$$
$$v_1 = -0.4375 \text{ m/s}$$

The negative sign indicates that the rifle recoils in the direction opposite to the bullet.

Answer: (b) (Difficulty: Easy)

Answer: (a) Accelerated - The train sped up while the coin was in the air. (Difficulty: Hard)

Answer: (b) Act on different bodies (Difficulty: Medium)

Answer: (c) Acceleration (Difficulty: Easy)

Answer: (c) (Difficulty: Medium)

Answer: 1 Newton is the amount of force that produces an acceleration of $1 \text{ m/s}^2$ in an object of mass 1 kg. ($1 \text{ N} = 1 \text{ kg} \cdot 1 \text{ m/s}^2$).

Answer: By lowering his hands, the cricketer increases the time taken to bring the high-velocity ball to rest. According to Newton's Second Law ($F = \frac{\text{Change in momentum}}{\text{Time}}$), increasing the time decreases the rate of change of momentum, thereby reducing the impact force on his hands.

Answer: Yes. According to Newton's First Law, if an object is already moving with a uniform velocity in a straight line, it will continue to do so even if the net force acting on it is zero (Balanced forces).

Answer: Momentum $p = mv$. Since momentum is directly proportional to velocity, if velocity is doubled, the momentum will also be doubled. (Difficulty: Easy)

Answer:

• Statement: The rate of change of momentum of an object is directly proportional to the applied unbalanced force in the direction of the force.
• Derivation: Consider an object of mass $m$ moving with initial velocity $u$. A force $F$ acts on it for time $t$, changing its velocity to $v$.
• Initial momentum, $p_1 = mu$
• Final momentum, $p_2 = mv$
• Change in momentum $= p_2 - p_1 = mv - mu = m(v - u)$
• Rate of change of momentum $= \frac{m(v - u)}{t}$
• According to the second law: $F \propto \frac{m(v - u)}{t}$
• Since $a = \frac{v - u}{t}$, we get $F \propto ma$
• $F = kma$ (where $k$ is a constant). If $k = 1$, then $F = ma$. (Difficulty: Hard)

Answer:

• Statement: In an isolated system, the total momentum before collision is equal to the total momentum after collision, provided no external force acts.
• Calculation:
• $m_1 = 1000 \text{ kg}$, $u_1 = 20 \text{ m/s}$, $v_1 = 15 \text{ m/s}$
• $m_2 = 1500 \text{ kg}$, $u_2 = 10 \text{ m/s}$, $v_2 = ?$
• $m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$
• $(1000 \times 20) + (1500 \times 10) = (1000 \times 15) + (1500 \times v_2)$
• $20000 + 15000 = 15000 + 1500v_2$
• $35000 = 15000 + 1500v_2$
• $20000 = 1500v_2$
• $v_2 = \frac{20000}{1500} = 13.33 \text{ m/s}$. (Difficulty: Hard)

a) Which law of physics explains the passengers being thrown forward? (Ans: Newton's First Law / Inertia of Motion)

b) How does a seatbelt prevent severe injuries based on Newton's Second Law?
(Ans: A seatbelt stretches slightly, increasing the 'time' it takes for the passenger to come to a halt. This decreases the rate of change of momentum, reducing the impact force). (Difficulty: Medium)

Answer: (A) Both are true, and R correctly explains A. (Difficulty: Easy)

Answer: (D) A is false, but R is true. They do not cancel out because they act on different bodies. (Difficulty: Hard)