Physics (Part-I) (UPSC)

1. When a parachutist jumps, the initial motion is free fall, so the speed increases as the distance fallen increases.
2. Air resistance also increases with speed, and eventually, a point is reached where the upward air resistance equals the downward gravitational force.
3. After this point, the speed becomes constant—this is called terminal velocity.
4. The graph showing this relationship starts with a rising slope (speed increasing with distance) and then flattens out (speed becomes constant) as distance increases.

So, the graph given in option (d) best represents the given situation.

Brahmagupta, an Indian mathematician and astronomer who lived in the 7th century, wrote in his text Brahmasphutasiddhanta that "bodies fall towards the earth...because it is in the nature of the earth to attract bodies...".
This statement predates Isaac Newton's work on the law of universal gravitation by over a thousand years and demonstrates an early understanding of the concept of gravity.
- Aryabhatta made significant contributions to mathematics and astronomy, including the concept of zero and a heliocentric model, but is not specifically credited with postulating about Earth's attraction force in this manner.
-Varahamihira was a renowned astronomer and astrologer but is not known for a similar statement about gravity.
- Brahmagupta's statement is a notable early observation about the earth's attractive property.

If a fluid flows such that its velocity at a point is always the same in magnitude and direction, the fluid is said to have a streamline flow. The type of flow in a fluid system is characterized by the presence of laminae, or parallel streams of fluid.
A streamline is a straight or curved path such that tangent to it at a point gives the direction of flow of liquid at that point. Thus, according to question the flow profile is best represented by figure (a).

Graph (a) correctly represents the displacement-time relationship for a freely falling object. As time increases, the displacement increases quadratically due to constant acceleration under gravity. Remember, the key insight is that free fall leads to quadratic displacement with respect to time.
• Gravity as the Only Force: The defining feature is that gravity is the only force acting; friction or air resistance must be negligible or absent.
• Constant Acceleration: All freely falling objects accelerate at the same rate, known as the acceleration due to gravity (g), approximately 9.8 m/s² on Earth, irrespective of their mass or size.
• Mass Independence: A heavier object and a lighter object (like a bowling ball and a feather in a vacuum) fall at the same rate because their increased mass is proportionally offset by the greater gravitational force on them.
• Equations of Motion: Their motion can be described using standard kinematic equations, where acceleration (a) is replaced by g.

A simple machine, such as a lever, pulley, or inclined plane, is a device that changes the direction or magnitude of a force.
It makes work easier by allowing you to apply a smaller force over a longer distance to achieve the same amount of work. It doesn't reduce the total work done, as work is defined as force multiplied by distance.

Surface tension is the cohesive force that exists at the surface of a liquid. It's caused by the attraction between the liquid molecules, which pulls them inward and makes the surface behave like a stretched elastic membrane.
This force minimizes the surface area of the liquid, which is why liquid drops in free fall, like raindrops, tend to form a spherical shape, as a sphere has the smallest surface area for a given volume.

Scalars are quantities that have magnitude only, they are independent of direction. Vectors have both magnitude and direction.
Momentum is the product of the mass and velocity of an object (p = mv) Momentum is a vector quantity, since it has a direction as well as a magnitude. The rest of quantities in option pressure, work and energy have magnitude but not direction.

The period of a simple pendulum (which a swing approximates) is determined by its length. The length of a pendulum is measured from the pivot point to the center of mass. When the girl stands up, her center of mass shifts upwards, closer to the pivot point of the swing.
This effectively shortens the length of the pendulum. Since the period of a pendulum is directly proportional to the square root of its length, shortening the length will decrease the period, causing the swing to oscillate faster.

The above diagram represents a body in projectile motion
Maximum height y max = (v² sin² θ)/(2g)
Thus, according to above equation greater the initial inclination, the greater is the height reached.
A projectile is any object thrown into space upon which the only acting force is gravity. The primary force acting on a projectile is gravity. This doesn’t necessarily mean that other forces do not act on it, just that their effect is minimal compared to gravity. The path followed by a projectile is known as a trajectory. A baseball batted or thrown is an example of a projectile.
When a particle is thrown obliquely near the earth's surface, it moves along a curved path under constant acceleration directed towards the centre of the earth (we assume that the particle remains close to the earth's surface). The path of such a particle is called a projectile, and the motion is called projectile motion.

A washing machine uses a process called centrifugation to separate water from the clothes. During the spin cycle, the drum rotates at a very high speed, creating a centrifugal force that pushes the clothes against the outer wall.
The water, being less dense, is forced out through the holes in the drum, leaving the clothes relatively dry.
Key Steps :

1. Filling & Detergent Action: Water enters the tub, mixing with detergent. Detergent's surfactants surround dirt particles (oil/grease) with a hydrophilic (water-loving) outer layer, trapping them.
2. Agitation (Wash Cycle): An internal agitator or paddles rotate, tumbling clothes in the soapy water. This mechanical action helps loosen dirt and stains from fabrics.
3. Draining: Dirty, soapy water is pumped out of the machine.
4. Rinsing: Clean water fills the drum, and the clothes are agitated again to rinse off residual soap and dirt.
5. Spinning (Centrifugation): The inner drum spins rapidly (800–1600 RPM). The resulting centrifugal force pushes the clothes against the drum wall, forcing water through the drum’s perforations and out of the machine, leaving clothes damp but cleaner and partially dry.