Physics: Mechanics: UPSC Previous Year Questions (Science and Technology)

Explanation

The question is based on the principle of buoyancy, which means that an object fully or partly immersed in fluid experiences an upthrust or buoyant force equal to the weight of the fluid displaced. When a weightless balloon filled with water is immersed into water, it displaces an amount of water equivalent to its own volume, in this case, 200 cc. The weight of this displaced water in terms of gravitational pull is equal to the weight of the balloon under these conditions. Since both weights are identical (as the balloon is also filled with water), they cancel out each other, resulting in a net weight of the balloon in water to be zero.

Explanation

Assertion (A) is true: Weight is the force of gravity acting on an object, and gravity weakens as the distance from the Earth>s center increases. Since altitude represents a greater distance from the Earth>s center, the force of gravity and thus the weight of the body diminish. Reason (R) is true: The Earth is not a perfect sphere, being slightly flattened at the poles and bulging at the equator, this fact does not primarily explain the decrease in weight with altitude. The primary reason lies in the inverse square law of gravity, which states that the force of gravity between two objects decreases proportionally to the square of the distance between them. Hence, Reason (R) does not correctly explain the Assertion (A).

Explanation

Statement 1 is correct: When a vehicle takes a sharp turn at high speed, the centrifugal force may push the vehicle outwards. This can cause the vehicle to tilt outwards and potentially overturn about its outer wheels.

Statement 2 is incorrect: This is less likely to happen. The centrifugal force pushes the vehicle outwards, not inwards.

Statement 3 is correct: If the friction between the tires and the road is insufficient to provide the necessary centripetal force, the vehicle may skid outwards, away from the center of the turn.

Statement 4 is incorrect: Skidding typically occurs outwards, not inwards, due to the centrifugal force.

Explanation

When the oil tanker accelerates forward, the oil inside experiences an inertial force (pseudo force) acting in the opposite direction to the acceleration. This causes the free surface of the oil to tilt. 1. The rear end of the tanker has larger depth because the inertial force pushes the oil backward.

2. The front end has smaller depth as the oil moves away from it. Thus, The free surface of the oil becomes inclined, with the rear end having a larger depth

Explanation

Density is a measure of how much mass is packed into a given volume. Buoyancy is the tendency of an object to float in a fluid. An object floats if its density is less than the fluid’s density and sinks if its density is greater. If the densities are equal, the object remains neutrally buoyant, neither sinking nor floating. Assertion (A) is true: Iron is denser than water, so it sinks in water. However, mercury is denser than iron, so an iron ball will float on mercury. Reason (R) is false: Specific gravity is the ratio of the density of a substance to the density of a reference substance (usually water). Mercury is denser than iron, so its specific gravity is higher.

Explanation

Statement 1 is correct: At the mean position, the pendulum has maximum velocity and is moving in a straight line for an instant with no force along its path and hence producing zero acceleration.

Statement 2 is correct: In one complete oscillation, the bob passes through the mean position twice - once moving in each direction, hence attaining the maximum velocity twice in a complete oscillation.

Statement 3 is incorrect: At the extreme position, the bob has zero velocity as it stops for an instant before reversing the direction. However, at this point the acceleration is maximum because bob completely comes under the force of gravity and hence produces maximum acceleration.

Statement 4 is correct: In an ideal situation, due to air resistance and internal friction, the amplitude of oscillation decreases with time.

Explanation

The motion of an object traveling in a straight line can be represented on a distance-time graph, with the shape of the graph depending on whether the motion is uniform (straight line) or non-uniform (curved line). Uniform motion represents a constant change in displacement per second. The distance time graph for uniform motion is a straight line, that is, equal distance is covered by the equal units of time.

Option (d) represents the graph where change in displacement per second is constant. Therefore, velocity is constant and hence it performs uniform motion.

Explanation

Option 1 is incorrect: While radial tyres improve handling and durability, they primarily reduce rolling resistance, which can have a minor impact on fuel efficiency. However, their primary benefit is not directly linked to significant fuel savings.

Option 2 is correct: A streamlined body reduces aerodynamic drag, allowing the car to move more efficiently through the air. This directly improves fuel efficiency, especially at higher speeds. An example of a car with a streamlined body is the Tesla Model S. Its sleek, aerodynamic design minimizes air resistance, improving both fuel efficiency (or energy efficiency in the case of electric cars) and performance.

Option 3 is correct: Multipoint Fuel Injection ensures that the right amount of fuel is injected into each cylinder, improving combustion efficiency and reducing fuel consumption.

Option 4 is incorrect: While a catalytic converter reduces harmful emissions, it does not directly affect fuel efficiency. Its primary function is to convert toxic gases like carbon monoxide into less harmful substances. Direction: The following item consists of two statements, one labeled as the Assertion (A) and the other as Reason (R). You have to answer these items using the code given below.

Explanation

According to Newton’s first law of motion, " A body at rest will remain at rest, and a body in motion will continue in uniform motion in a straight line unless acted upon by an external force". According to Newton’s second law of motion, "The rate of change of momentum of a body is directly proportional to the applied force and occurs in the direction of the force". Assertion (A) is true: When the man whistles, he expels air from his lungs. This expelled air has mass and velocity, creating momentum in the forward direction and thus creating reaction force which pushes the man backward on the frictionless surface. This is based on Newton’s second law of motion. Reason (R) is true: The statement that ‘ if no external force acts on a system, its momentum cannot change’ is clearly stating Newton>s first law of motion which is clearly not explaining the Assertion (A). Thus, Reason (R) merely states Newton’s First Law of Motion and doen’s explain the Assertion (A) which is based on Newton’s Second Law of Motion.

Explanation

Both the bullet and the monkey experience the same downward acceleration due to gravity provided the air resistance is negligible. When the hunter fires the bullet, the bullet starts moving along a curved trajectory due to the combined effects of its horizontal velocity and the vertical acceleration caused by gravity. When the monkey jumps, it also begins to fall freely under gravity with an initial vertical velocity of zero. Since the hunter aims directly at the monkey at the moment of firing, the bullet and the monkey will both fall the same vertical distance due to gravity at the same time. Therefore, the bullet will hit the monkey at the point aimed.