GIKI Admission Test Physics Syllabus

On a velocity-time graph, what do the slope and the area under the curve represent?

The slope (gradient) gives acceleration; the area under the graph gives displacement.

For a body falling freely from rest, what is the distance fallen and velocity after time t (g = 9.8 m/s²)?

Distance h = ½gt² and velocity v = gt (taking u = 0). Acceleration equals g downward, independent of mass.

State Newton's three laws of motion.

1st: A body stays at rest or in uniform motion unless acted on by a net external force (inertia). 2nd: F = ma (net force equals rate of change of momentum). 3rd: Every action has an equal and opposite reaction.

State Newton's second law in terms of momentum.

The net force equals the rate of change of momentum: F = Δp/Δt = d(mv)/dt. For constant mass this reduces to F = ma.

Why do action and reaction forces never cancel each other out?

Because they act on two different bodies, not the same one. Only forces acting on the same body can be added to give a net force.

What is the apparent weight of a person of mass m in a lift accelerating upward with acceleration a?

Apparent weight (normal reaction) R = m(g + a). It is m(g − a) when accelerating downward, and zero (weightlessness) during free fall (a = g).

For projectile motion, what are the horizontal and vertical components of velocity, and how do they change?

Horizontal: vₓ = u cos θ, constant (no horizontal acceleration). Vertical: vᵧ = u sin θ − gt, changing due to gravity g downward.

Give the formulas for the maximum height, time of flight, and range of a projectile launched at angle θ with speed u.

Max height H = u²sin²θ /(2g); Time of flight T = 2u sinθ /g; Range R = u²sin2θ /g.

At what launch angle is the range of a projectile maximum, and what is that maximum range?

Range is maximum at θ = 45°, giving R_max = u²/g. Complementary angles (e.g., 30° and 60°) give the same range.

Define centripetal acceleration and give its formula for circular motion.

Centripetal acceleration is directed toward the centre of the circle: a꜀ = v²/r = ω²r, where v is linear speed, ω is angular speed, and r is radius.

What is centripetal force, and what provides it for a car turning on a flat road and for a satellite?

Centripetal force F = mv²/r = mω²r, directed toward the centre. For a car it is provided by friction; for a satellite it is provided by gravity.

Relate linear quantities to angular quantities in rotational motion (v, a, and the equation of motion).

v = rω (linear speed), a = rα (tangential acceleration). Rotational analog: ω = ω₀ + αt, with τ = Iα (torque = moment of inertia × angular acceleration).

Define moment of inertia and angular momentum.

Moment of inertia I = Σmr² measures resistance to angular acceleration (rotational inertia). Angular momentum L = Iω; it is conserved when no external torque acts.

Define work and state when work done is zero, positive, and negative.

Work W = F s cos θ. It is zero when force is perpendicular to displacement (θ = 90°), positive when θ < 90°, and negative when θ > 90° (force opposes motion).

State the work-energy theorem.

The net work done on a body equals the change in its kinetic energy: W_net = ΔKE = ½mv² − ½mu².

Give the formulas for kinetic energy and gravitational potential energy.

Kinetic energy KE = ½mv². Gravitational potential energy PE = mgh (relative to a reference level).

State the law of conservation of energy.

Energy cannot be created or destroyed, only transformed from one form to another; the total energy of an isolated system remains constant.

For a body falling freely (ignoring air resistance), how do KE and PE change, and what stays constant?

As it falls, PE decreases and KE increases by the same amount, so total mechanical energy (KE + PE) stays constant. At any height: mgh + ½mv² = constant.

Define power and give its formula in terms of work and in terms of force and velocity.

Power is the rate of doing work: P = W/t. It also equals P = F·v (force times velocity). SI unit is the watt (W = J/s); 1 hp ≈ 746 W.

Define linear momentum and state the law of conservation of momentum.

Momentum p = mv (a vector). Conservation: in the absence of external forces, the total momentum of a system before a collision equals that after the collision.

Distinguish between elastic and inelastic collisions.

In elastic collisions both momentum AND kinetic energy are conserved. In inelastic collisions momentum is conserved but kinetic energy is not (some converts to heat/deformation); in a perfectly inelastic collision the bodies stick together.

Define impulse and state its relationship to momentum.

Impulse = F·Δt = change in momentum (Δp). It equals the area under a force-time graph; SI unit is N·s (same as kg·m/s).

Define density and pressure, and give the formula for pressure due to a liquid column of height h.

Density ρ = mass/volume. Pressure P = force/area. Pressure at depth h in a liquid: P = ρgh (gauge pressure), independent of container shape.

State Pascal's principle and Archimedes' principle.

Pascal's principle: pressure applied to an enclosed fluid is transmitted undiminished throughout. Archimedes' principle: the upthrust (buoyant force) on a body equals the weight of the fluid it displaces.

What is the equation of continuity for an incompressible fluid, and what does it imply?

A₁v₁ = A₂v₂ (volume flow rate is constant). It implies fluid speed increases where the cross-sectional area decreases (narrow pipes = faster flow).

State Bernoulli's equation and the assumptions behind it.

P + ½ρv² + ρgh = constant, for an ideal fluid that is incompressible, non-viscous, and in steady (streamline) flow.

Explain, using Bernoulli's principle, why an aeroplane wing generates lift.

Air moves faster over the curved top of the wing than underneath, so by Bernoulli's principle pressure on top is lower than below. The pressure difference produces a net upward force (lift).

Define viscosity and state Stokes' law for a sphere falling through a fluid.

Viscosity is a fluid's internal resistance to flow (friction between layers). Stokes' law: drag force F = 6πηrv, where η is viscosity, r the sphere radius, and v its speed.

What is terminal velocity, and how does it arise for a sphere falling in a viscous fluid?

Terminal velocity is the constant maximum speed reached when the net force is zero, i.e., when weight = upthrust + viscous drag, so acceleration becomes zero.

Define surface tension and explain why small liquid drops are spherical.

Surface tension is the force per unit length acting along a liquid surface (or surface energy per unit area) due to cohesive forces. Drops are spherical because a sphere has the minimum surface area for a given volume, minimizing surface energy.

Define Simple Harmonic Motion (SHM) and give the defining relationship between acceleration and displacement.

SHM is oscillatory motion where acceleration is directly proportional to displacement from the mean position and directed toward it: a = −ω²x. Equivalently, the restoring force F = −kx.

Give the formulas for the time period of a mass-spring system and a simple pendulum.

Mass-spring: T = 2π√(m/k). Simple pendulum: T = 2π√(L/g), where L is length and g is gravitational acceleration. Pendulum period is independent of mass and (small) amplitude.

In SHM, where are velocity and acceleration maximum and where are they zero?

Velocity is maximum at the mean (equilibrium) position and zero at the extremes. Acceleration is maximum at the extremes and zero at the mean position. v_max = ωA and a_max = ω²A.

Distinguish between free, damped, and forced oscillations.

Free oscillations occur at the natural frequency with no external force (constant amplitude, ideally). Damped oscillations lose energy so amplitude decays. Forced oscillations are driven by a periodic external force at the driver's frequency.

What is resonance, and when does it occur?

Resonance occurs when the driving (forcing) frequency equals the natural frequency of the system, producing maximum amplitude and maximum energy transfer.

Distinguish between transverse and longitudinal waves, with an example of each.

In transverse waves particles vibrate perpendicular to wave travel (e.g., light, water ripples, string waves). In longitudinal waves particles vibrate parallel to wave travel, forming compressions and rarefactions (e.g., sound).

State the wave equation relating speed, frequency, and wavelength, and define wavelength.

v = fλ, where v is wave speed, f is frequency, and λ is wavelength (the distance between two consecutive points in phase, e.g., crest to crest).

State the principle of superposition of waves.

When two or more waves overlap, the resultant displacement at any point equals the vector sum of the individual displacements of the waves at that point.

Distinguish between constructive and destructive interference in terms of path difference.

Constructive interference (maximum amplitude) occurs when the path difference is a whole number of wavelengths (nλ). Destructive interference (minimum/zero amplitude) occurs at odd half-wavelength path differences ((n+½)λ).

What is a stationary (standing) wave, and how is it formed?

A standing wave forms when two identical waves travel in opposite directions and superpose, producing fixed nodes (zero amplitude) and antinodes (maximum amplitude). No net energy is transported along the wave.