Daily Olympiad: Science - Force and Laws of Motion [20260524]

Solution

Correct: A

Newton's First Law of Motion, also known as the Law of Inertia, states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. This law directly defines and explains the concept of inertia.

Solution

Correct: B

According to Newton's Second Law of Motion, Force (F) = mass (m) × acceleration (a). Given F = 10 N and m = 2 kg. So, a = F / m = 10 N / 2 kg = 5 m/s².

Solution

Correct: C

When the bus is moving, the passenger is also in a state of motion along with the bus. When the brakes are applied suddenly, the bus slows down, but due to inertia of motion, the passenger's body tends to continue in its state of motion, causing them to jerk forward.

Solution

Correct: C

Momentum (p) is defined as the product of mass (m) and velocity (v), i.e., p = m × v. The S.I. unit of mass is kilogram (kg) and the S.I. unit of velocity is meter per second (m/s). Therefore, the S.I. unit of momentum is kilogram meter per second (kg m/s).

Solution

Correct: A

The Law of Conservation of Momentum states that for a closed system, the total momentum before collision is equal to the total momentum after collision. Before collision, total momentum = m1v1 + m2v2. After collision, since they stick together, their combined mass is (m1 + m2) and they move with a common velocity, say V. So, total momentum after collision = (m1 + m2)V. Equating them: m1v1 + m2v2 = (m1 + m2)V. Therefore, V = (m1v1 + m2v2) / (m1 + m2).

Solution

Correct: C

An unbalanced force causes a change in the state of motion (speed or direction) of an object. A ball rolling to a stop on a grassy field is decelerating due to the force of friction, which is an unbalanced force acting opposite to its motion. In the other cases, the net force is zero (constant velocity or at rest). While a satellite orbiting Earth is constantly changing direction, implying an unbalanced force (gravitational force), its speed is constant (in uniform circular motion), which can make it confusing for this level. The deceleration of a rolling ball is a clearer example of an unbalanced force causing a change in speed.

Solution

Correct: C

Newton's Third Law states that action and reaction forces are equal in magnitude and opposite in direction. However, a crucial aspect is that they always act on different bodies. For example, if you push a wall (action), the wall pushes back on you (reaction). These forces do not cancel each other out because they act on different objects.

Solution

Correct: C

In a vacuum, there is no air resistance. Therefore, the only force acting on both the feather and the stone is gravity. Since the acceleration due to gravity (g) is constant for all objects regardless of their mass, both the feather and the stone will fall at the same rate and reach the ground at the same time.

Solution

Correct: D

When pulling a lawnmower, the upward component of the pulling force reduces the normal force exerted by the ground on the lawnmower. Since frictional force is directly proportional to the normal force, a reduced normal force leads to reduced friction, making it easier to pull. Conversely, when pushing, the downward component of the pushing force increases the normal force, thus increasing friction.

Solution

Correct: C

Weight (W) is the force exerted on an object due to gravity, and it is calculated as W = mass (m) × acceleration due to gravity (g). Given m = 50 kg and g = 9.8 m/s². So, W = 50 kg × 9.8 m/s² = 490 N.

Solution

Correct: A

Static friction is the friction that prevents an object from moving when a force is applied. It is generally greater than kinetic (sliding) friction, which acts on an object once it is already in motion. This is why it takes more force to start an object moving than to keep it moving.

Solution

Correct: B

According to the Law of Conservation of Momentum, the total momentum before firing (0) equals the total momentum after firing. Let m_b = 0.01 kg (mass of bullet), v_b = 500 m/s (velocity of bullet), m_g = 5 kg (mass of gun), v_g = recoil velocity of gun. So, 0 = (m_b × v_b) + (m_g × v_g). 0 = (0.01 kg × 500 m/s) + (5 kg × v_g). 0 = 5 kg m/s + 5 kg × v_g. 5 kg × v_g = -5 kg m/s. v_g = -5/5 = -1 m/s. The negative sign indicates the recoil is in the opposite direction to the bullet's motion.

Solution

Correct: C

Momentum (p) = mass (m) × velocity (v). If velocity (v) is doubled to 2v, and mass (m) remains constant, the new momentum p' = m × (2v) = 2(mv) = 2p. Thus, the momentum is doubled.

Solution

Correct: B

Spikes on shoes increase the grip between the shoes and the ground. This increased grip is due to an increase in the force of friction. Higher friction allows athletes to push against the ground with more force without slipping, thus generating more forward propulsion and better performance.

Solution

Correct: C

According to Newton's First Law, an object continues in its state of rest or uniform motion in a straight line unless acted upon by an unbalanced force. If an object is moving at a constant velocity (meaning constant speed and constant direction), its acceleration is zero. According to Newton's Second Law (F=ma), if acceleration (a) is zero, then the net force (F) acting on the object must also be zero.

Solution

Correct: C

Inertia is directly proportional to mass. The greater the mass of an object, the greater its inertia (its resistance to changes in its state of motion). Among the given options, a fully loaded train has the largest mass, and therefore, the greatest inertia.

Solution

Correct: C

According to Newton's Second Law, F = ma, or a = F/m. If the force (F) is doubled to 2F, and the mass (m) remains constant, the new acceleration a' = (2F)/m = 2(F/m) = 2a. Thus, the acceleration is doubled.

Solution

Correct: C

This phenomenon is a direct application of Newton's Third Law of Motion. When the person pushes on the wall (action force), the wall exerts an equal and opposite force back on the person (reaction force), causing them to move backward on the skateboard.

Solution

Correct: B

Impulse (J) is defined as the product of force (F) and the time interval (Δt) over which the force acts (J = F × Δt). According to Newton's Second Law, F = Δp/Δt (rate of change of momentum). Therefore, F × Δt = Δp. This means impulse is equal to the change in momentum (J = Δp). This is also known as the impulse-momentum theorem.

Solution

Correct: D

Seatbelts are designed to protect passengers by preventing them from being thrown forward due to inertia during a sudden stop or collision. By restraining the body, the seatbelt applies a force over a longer period, reducing the magnitude of the force experienced by the body (as per the impulse-momentum theorem, FΔt = Δp, so if Δt increases, F decreases for the same Δp), thus minimizing injury.