FBISE Examinations Physics (HSSC) Syllabus

State the head-to-tail rule for vector addition.

Place vectors so the tail of each successive vector touches the head of the previous one; the resultant is drawn from the tail of the first vector to the head of the last vector.

How are the rectangular components Ax and Ay of a vector A making angle θ with the x-axis found?

Ax = A cos θ and Ay = A sin θ.

Given components Ax and Ay, how do you find the magnitude and direction of the vector?

Magnitude A = √(Ax² + Ay²); Direction θ = tan^-1(Ay / Ax) measured from the x-axis.

What is a unit vector and how is it obtained from a vector A?

A unit vector has magnitude 1 and indicates direction only. It is obtained by = A / |A|.

What are the unit vectors î, ĵ, and k̂?

They are unit vectors directed along the positive x, y, and z axes respectively, each with magnitude 1.

Define the scalar (dot) product of two vectors and give its formula.

The scalar product A·B = AB cos θ, where θ is the angle between them. It yields a scalar quantity.

What are the dot products î·î and î·ĵ?

î·î = ĵ·ĵ = k̂·k̂ = 1 (parallel, cos 0° = 1); î·ĵ = ĵ·k̂ = k̂·î = 0 (perpendicular, cos 90° = 0).

Define the vector (cross) product of two vectors and give its formula.

The vector product A×B = AB sin θ n̂, where θ is the angle between them and n̂ is the unit vector perpendicular to the plane of A and B (given by the right-hand rule). It yields a vector.

What is the direction of the cross product determined by?

The right-hand rule: curl the fingers of the right hand from A toward B; the thumb points in the direction of A×B.

State two key differences between dot product and cross product.

Dot product gives a scalar and uses cos θ; it is commutative (A·B = B·A). Cross product gives a vector and uses sin θ; it is anti-commutative (A×B = -B×A).

What is the cross product of two parallel vectors and of two perpendicular vectors?

Parallel vectors: A×B = 0 (sin 0° = 0). Perpendicular vectors: A×B = AB (sin 90° = 1, maximum).

Define torque and give its formula.

Torque (moment of force) is the turning effect of a force about a point. τ = r × F, with magnitude τ = rF sin θ = (force) × (moment arm).

What is the SI unit of torque and is it a scalar or vector?

The SI unit of torque is the newton-metre (N·m). Torque is a vector quantity.

What is the moment arm of a force?

The moment arm is the perpendicular distance from the axis of rotation (pivot) to the line of action of the force.

State the first condition of equilibrium.

The vector sum of all forces acting on a body must be zero: ΣF = 0, i.e., ΣFx = 0 and ΣFy = 0. This ensures translational equilibrium.

State the second condition of equilibrium.

The vector sum of all torques acting on a body about any point must be zero: Στ = 0. This ensures rotational equilibrium.

Distinguish between the three states of equilibrium.

Stable equilibrium: body returns to original position after slight displacement (CG rises). Unstable: body moves further away (CG falls). Neutral: body stays in new position (CG remains same height).

State Newton's first law of motion.

A body at rest remains at rest, and a body in motion continues in uniform motion in a straight line, unless acted upon by a net external force. (Law of inertia.)

State Newton's second law of motion and give its equation.

The rate of change of momentum of a body is directly proportional to the applied force and is in the direction of the force: F = ma (or F = Δp/Δt).

State Newton's third law of motion.

To every action there is an equal and opposite reaction; the action and reaction forces act on two different bodies.

Define linear momentum, give its formula, SI unit, and state whether it is a vector.

Linear momentum p = mv (mass × velocity). SI unit: kg·m·s^-1. It is a vector quantity in the direction of velocity.

Define impulse and state the impulse-momentum theorem.

Impulse = force × time of contact = F·Δt. The impulse-momentum theorem states impulse equals the change in momentum: FΔt = Δp = mv - mu. SI unit: N·s.

State the law of conservation of momentum.

For an isolated system (no external force), the total linear momentum remains constant before and after an interaction: m1u1 + m2u2 = m1v1 + m2v2.

What is the difference between an elastic and an inelastic collision?

In an elastic collision both momentum and kinetic energy are conserved. In an inelastic collision momentum is conserved but kinetic energy is not (some converts to heat/sound/deformation).

What is projectile motion?

Projectile motion is the two-dimensional motion of a body thrown into the air at an angle, moving under gravity alone, following a parabolic path. Horizontal velocity is constant; vertical motion has acceleration g downward.

For a projectile launched with speed v at angle θ, give the formula for time of flight.

Time of flight T = (2 v sin θ) / g.

For a projectile launched with speed v at angle θ, give the formula for maximum height.

Maximum height H = (v² sin²θ) / (2g).

For a projectile launched with speed v at angle θ, give the formula for horizontal range and the angle for maximum range.

Range R = (v² sin 2θ) / g. Maximum range occurs at θ = 45°, giving R(max) = v²/g.

Define work done by a constant force and give its formula.

Work is done when a force moves a body through a displacement. W = F·d = Fd cos θ, where θ is the angle between force and displacement. SI unit: joule (J). Work is a scalar.

How is the work done by a variable force determined?

It equals the area under the force–displacement (F–d) graph, or mathematically W = ∫F dx (the integral of force with respect to displacement).

Define power and efficiency, giving their formulas and units.

Power is the rate of doing work: P = W/t (also P = F·v); SI unit watt (W). Efficiency = (useful output energy / total input energy) × 100%, a dimensionless ratio (often given as a percentage).