FSc Pre-Medical Physics Syllabus

Are leading zeros significant? (e.g., 0.0045)

No, zeros to the left of the first non-zero digit are not significant; 0.0045 has 2 significant figures.

Are trailing zeros after a decimal point significant? (e.g., 2.300)

Yes, trailing zeros after a decimal point are significant; 2.300 has 4 significant figures.

State the rule for significant figures when multiplying or dividing.

The result should have as many significant figures as the measurement with the fewest significant figures.

State the rule for significant figures when adding or subtracting.

The result should have the same number of decimal places as the measurement with the fewest decimal places.

Distinguish between scalar and vector quantities.

A scalar has only magnitude (e.g., mass, time, energy); a vector has both magnitude and direction (e.g., displacement, force, velocity).

State the head-to-tail rule for adding vectors.

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

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

Ax = A cosθ (horizontal component) and Ay = A sinθ (vertical component).

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

Magnitude: A = √(Ax² + Ay²); Direction: θ = tan⁻¹(Ay/Ax).

How is a vector A expressed in terms of unit vectors?

A = Ax î + Ay ĵ + Az k̂, where î, ĵ, k̂ are unit vectors along the x, y, z axes.

What is a unit vector and how is it obtained?

A unit vector has magnitude 1 and shows direction; it is obtained by dividing a vector by its own magnitude: â = A/|A|.

Define the dot (scalar) product of two vectors.

A·B = AB cosθ, where θ is the angle between them; the result is a scalar.

Define the cross (vector) product of two vectors.

A×B = AB sinθ n̂, where θ is the angle between them and n̂ is a unit vector perpendicular to the plane of A and B (direction by right-hand rule); the result is a vector.

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

Perpendicular: A·B = 0 (cos90°=0); Parallel: A·B = AB (cos0°=1).

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

Parallel: A×B = 0 (sin0°=0); Perpendicular: |A×B| = AB (sin90°=1).

Is the cross product commutative? State the relation.

No; A×B = −(B×A), so it is anti-commutative.

Give an example of a physical quantity defined by a dot product and one by a cross product.

Dot product: Work, W = F·d; Cross product: Torque, τ = r×F (also angular momentum L = r×p).

Define torque (moment of force).

Torque is the turning effect of a force about a point or axis; τ = rF sinθ, where r is the moment arm and θ the angle between r and F. SI unit: N·m.

State the first condition of equilibrium.

The vector sum of all forces acting on a body is zero: ΣF = 0 (i.e., ΣFx = 0 and ΣFy = 0).

State the second condition of equilibrium.

The vector sum of all torques acting on the body about any point is zero: Στ = 0.

Distinguish between translational and rotational equilibrium.

Translational equilibrium: net force is zero (no linear acceleration); rotational equilibrium: net torque is zero (no angular acceleration).

Define displacement and how it differs from distance.

Displacement is the shortest straight-line vector from initial to final position (has direction); distance is the total path length (a scalar).

Distinguish between average velocity and instantaneous velocity.

Average velocity = total displacement/total time; instantaneous velocity is the velocity at a particular instant (limit of average velocity as time interval approaches zero).

Define acceleration and give its SI unit.

Acceleration is the rate of change of velocity, a = Δv/Δt; SI unit is m/s². It is a vector quantity.

State the three equations of uniformly accelerated motion.

vf = vi + at; S = vi t + ½ a t²; 2aS = vf² − vi².

State Newton's first law of motion.

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

State Newton's second law of motion.

The rate of change of momentum of a body is directly proportional to the applied net force and is in the direction of that force; F = ma.

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 and give its formula and SI unit.

Linear momentum is the product of mass and velocity, p = mv; it is a vector with SI unit kg·m/s. It is the quantity of motion of a body.

State the law of conservation of linear momentum.

If no external force acts on a system, the total linear momentum of the system remains constant: total momentum before collision = total momentum after collision.

Distinguish between elastic and inelastic collisions.

In an elastic collision both momentum and kinetic energy are conserved; in an inelastic collision momentum is conserved but kinetic energy is not.

Define impulse and state its relation to momentum.

Impulse = force × time of contact = FΔt; it equals the change in momentum: FΔt = Δp. SI unit: N·s.

What is projectile motion?

Two-dimensional motion of a body under gravity after being projected, having a constant horizontal velocity and a vertically accelerated motion (a = g downward).

For a projectile launched at angle θ with speed v, what are the initial horizontal and vertical velocity components?

Horizontal: vx = v cosθ (constant); Vertical: vy = v sinθ (changes due to gravity).

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

Time of flight T = (2v sinθ)/g; Maximum height H = (v² sin²θ)/(2g); Range R = (v² sin2θ)/g.

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

At 45°, because R = (v² sin2θ)/g is maximum when sin2θ = 1, i.e., 2θ = 90°.

Define work and state when work done by a force is zero.

Work W = F·d = Fd cosθ (force times displacement in force direction). Work is zero when θ = 90° (force perpendicular to displacement) or when displacement is zero. SI unit: joule (J).

Define kinetic energy and give its formula.

Kinetic energy is the energy possessed by a body due to its motion; K.E. = ½ m v².

State the work-energy principle (theorem).

The net work done on a body equals the change in its kinetic energy: W = ΔK.E. = ½ m vf² − ½ m vi².

Define gravitational potential energy and give its formula.

It is the energy stored in a body due to its position/height in a gravitational field; P.E. = mgh.

Define power and give its SI unit and formula.

Power is the rate of doing work, P = W/t = F·v; SI unit is the watt (W), where 1 W = 1 J/s.