PIEAS Admission Test Physics Syllabus

Write the three equations of motion for uniform acceleration.

v = u + at; s = ut + (1/2)at^2; v^2 = u^2 + 2as, where u is initial velocity, v final velocity, a acceleration, s displacement, t time.

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

The slope represents acceleration; the area under the curve represents displacement.

For a freely falling body (taking down as positive), what value replaces a, and what is the initial velocity if dropped from rest?

a = g = 9.8 m/s^2 (acceleration due to gravity); initial velocity u = 0 when dropped from rest.

In two-dimensional motion, why can horizontal and vertical motions be treated independently?

Because the perpendicular components of motion are independent: a force/acceleration in one direction does not affect motion in the perpendicular direction (principle of independence of motions).

Define projectile motion and state the path it follows.

Projectile motion is the motion of a body launched into the air subject only to gravity (no air resistance); it follows a parabolic path.

For a projectile launched at speed v0 and angle theta, what are its initial horizontal and vertical velocity components?

Horizontal: vx = v0 cos(theta) (constant); vertical: vy = v0 sin(theta) (changes due to gravity).

Give the formulas for maximum height and time of flight of a projectile (launched and landing at the same level).

Maximum height H = (v0^2 sin^2(theta)) / (2g); time of flight T = (2 v0 sin(theta)) / g.

Give the formula for the horizontal range of a projectile and the angle for maximum range.

Range R = (v0^2 sin(2theta)) / g; maximum range occurs at theta = 45 degrees.

State Newton's First Law of Motion (law of inertia).

A body remains at rest or in uniform motion in a straight line unless acted upon by a net external force.

State Newton's Second Law of Motion in equation form.

The net force equals the rate of change of momentum: F = dp/dt; for constant mass, F = ma.

State Newton's Third Law of Motion.

For every action there is an equal and opposite reaction; the forces act on two different bodies, are equal in magnitude and opposite in direction.

Define inertia and state which physical quantity measures it.

Inertia is the tendency of a body to resist any change in its state of rest or uniform motion; mass is the measure of inertia.

Define linear momentum and give its SI unit.

Linear momentum p = mv (mass times velocity); it is a vector. SI unit: kg m/s (or N s).

State the law of conservation of linear momentum.

If no net external force acts on a system, its total linear momentum remains constant (the total momentum before equals the total momentum after an interaction).

Define impulse and state the impulse-momentum theorem.

Impulse = force x time = F(delta t); the impulse-momentum theorem states impulse equals the change in momentum: F(delta t) = delta p.

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 perfectly inelastic collisions the bodies stick together.

For a 1-D elastic collision of two bodies, what happens to velocities when the masses are equal?

When masses are equal in a 1-D elastic collision, the two bodies exchange velocities.

Define work and give its formula when force and displacement are at an angle.

Work is the product of displacement and the force component along it: W = F d cos(theta). SI unit: joule (J). It is a scalar.

State the work-energy theorem.

The net work done on a body equals the change in its kinetic energy: W_net = (1/2)mv^2 - (1/2)mu^2 = delta KE.

Give the formulas for kinetic energy and gravitational potential energy.

Kinetic energy KE = (1/2)mv^2; gravitational potential energy (near Earth) PE = mgh.

What is the difference between conservative and non-conservative forces? Give one example of each.

Conservative forces do work independent of path and store recoverable PE (e.g., gravity, spring force); non-conservative forces depend on path and dissipate energy (e.g., friction, air resistance).

State the law of conservation of mechanical energy.

In the absence of non-conservative forces, the total mechanical energy (KE + PE) of a system remains constant.

A body falls freely from height h. What is its speed just before hitting the ground (using energy conservation)?

By energy conservation mgh = (1/2)mv^2, so v = sqrt(2gh).

Define power and give two equivalent formulas.

Power is the rate of doing work or transferring energy: P = W/t, and also P = F v (force times velocity). SI unit: watt (W).

Define efficiency and give its formula.

Efficiency is the ratio of useful output energy (or power) to total input energy (or power): efficiency = (useful output / total input) x 100%. It is always less than 100% in real machines.

Define angular displacement, angular velocity, and angular acceleration with their units.

Angular displacement (theta, radian); angular velocity omega = d(theta)/dt (rad/s); angular acceleration alpha = d(omega)/dt (rad/s^2).

State the relations linking linear and angular quantities for circular motion.

Arc length s = r(theta); linear speed v = r(omega); tangential acceleration a = r(alpha), where r is the radius.

What is centripetal acceleration, and what are its formulas?

Centripetal acceleration is directed toward the centre of the circular path: a_c = v^2 / r = r(omega)^2.

Define centripetal force and give its formula. In what direction does it act?

Centripetal force is the net inward force keeping a body in circular motion: F_c = mv^2 / r = m r(omega)^2; it acts toward the centre of the circle.

State Newton's Law of Universal Gravitation in words and as an equation.

Every two point masses attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them: F = G(m1 m2) / r^2, where G is the universal gravitational constant (6.67 x 10^-11 N m^2/kg^2).

Derive the expression for the acceleration due to gravity g at Earth's surface from the law of gravitation.

Equating mg = G(Me m)/Re^2 gives g = G Me / Re^2, where Me is Earth's mass and Re its radius. This shows g is independent of the falling body's mass.