COMSATS Admission Test Physics Syllabus

Define instantaneous velocity and instantaneous acceleration.

Instantaneous velocity is the rate of change of displacement at an instant (v = dx/dt). Instantaneous acceleration is the rate of change of velocity at an instant (a = dv/dt).

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.

State 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 is final velocity, a is acceleration, t is time, and s is displacement.

What is the equation for displacement in the nth second of uniformly accelerated motion?

s_nth = u + (a/2)(2n - 1), where u is initial velocity, a is acceleration, and n is the second number.

For an object in free fall released from rest, what are its velocity and distance fallen after time t (taking g = 9.8 m/s^2)?

Velocity v = gt; distance fallen s = (1/2)gt^2, taking downward as positive and initial velocity zero.

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

Because the perpendicular components of motion are independent of each other; the equations of motion apply separately to each axis, sharing only the common variable of time.

What are the horizontal and vertical components of velocity throughout projectile motion (ignoring air resistance)?

The horizontal velocity (ux = u cos(theta)) stays constant; the vertical velocity (uy = u sin(theta)) changes due to gravity, decreasing on the way up and increasing on the way down.

State the formula for the time of flight of a projectile launched at angle theta with speed u.

T = (2u sin(theta)) / g.

State the formula for the maximum height of a projectile launched at angle theta with speed u.

H = (u^2 sin^2(theta)) / (2g).

State the formula for the horizontal range of a projectile launched at angle theta with speed u.

R = (u^2 sin(2theta)) / g.

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

At 45 degrees, because range R = (u^2 sin(2theta))/g is maximum when sin(2theta) = 1, i.e., 2theta = 90 degrees.

What is the shape of a projectile's trajectory and what is its velocity at the highest point?

The trajectory is a parabola. At the highest point the vertical velocity is zero and the velocity equals the horizontal component u cos(theta).

State Newton's first law of motion and define inertia.

A body remains at rest or in uniform motion in a straight line unless acted on by a net external force. Inertia is the property of a body to resist changes in its state of motion; it is measured by mass.

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

The rate of change of momentum of a body is directly proportional to the net applied force and is in the direction of that force. In equation form, F = ma (or F = dp/dt).

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.

What is the difference between mass and weight?

Mass is the amount of matter in a body (scalar, in kg, constant everywhere). Weight is the gravitational force on the body, W = mg (vector, in newtons), and varies with g.

Define the newton as the SI unit of force.

One newton is the force that gives a mass of 1 kilogram an acceleration of 1 metre per second squared (1 N = 1 kg m/s^2).

Define linear momentum and state its SI unit.

Linear momentum p = mv is the product of a body's mass and velocity; it is a vector. Its SI unit is kg m/s (or N s).

State the law of conservation of linear momentum.

In the absence of a net external force, the total linear momentum of an isolated system remains constant before and after any interaction or collision.

Define impulse and state the impulse-momentum theorem.

Impulse = force x time of contact (J = F*t). The impulse-momentum theorem states that impulse equals the change in momentum: F*t = m*v - m*u.

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 is converted to heat, sound, or deformation); in a perfectly inelastic collision the bodies stick together.

For a one-dimensional elastic collision of mass m1 (velocity u1) with stationary mass m2, what is the special case when m1 = m2?

When equal masses collide elastically and one is initially at rest, they exchange velocities: the moving body stops and the target moves off with the original velocity.

Define work done by a constant force and give the formula including angle.

Work is the product of the force and the displacement in the direction of the force: W = F s cos(theta), where theta is the angle between force and displacement. Its SI unit is the joule (J).

When is work done by a force zero?

Work is zero when there is no displacement, when the force is zero, or when the force is perpendicular to the displacement (theta = 90 degrees, cos 90 = 0).

Define kinetic energy and state its formula.

Kinetic energy is the energy a body possesses due to its motion: KE = (1/2)mv^2, where m is mass and v is speed.

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.

Define gravitational potential energy near the Earth's surface and give its formula.

Gravitational potential energy is the energy stored in a body due to its position in a gravitational field: PE = mgh, where m is mass, g is gravitational acceleration, and h is height above the reference level.

State the principle (law) of conservation of energy.

Energy can neither be created nor destroyed but only transformed from one form to another; the total energy of an isolated system remains constant.

For a body falling freely from height h, write the conservation-of-energy equation relating its speed at any point.

mgh = (1/2)mv^2 + mgh', so total mechanical energy mgh = (1/2)mv^2 + (potential energy at that point); at the ground v = sqrt(2gh).

Define power and give its formulas including the form involving force and velocity.

Power is the rate of doing work: P = W/t. It can also be written P = F v (force times velocity for motion in the direction of the force). SI unit is the watt (W = J/s).

Define efficiency and give its formula as a percentage.

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% due to energy losses.

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

Angular displacement (theta) is the angle swept, in radians. Angular velocity (omega = dtheta/dt) is the rate of change of angle, in rad/s. Angular acceleration (alpha = domega/dt) is the rate of change of angular velocity, in rad/s^2.

State the relationships linking linear and angular quantities (arc, speed, acceleration).

s = r*theta (arc length), v = r*omega (tangential speed), and a_t = r*alpha (tangential acceleration), where r is the radius.

What is centripetal acceleration and what are its formulas?

Centripetal acceleration is the inward (radial) acceleration of a body in circular motion, directed toward the centre: a_c = v^2/r = r*omega^2.

State the formula for centripetal force and give its direction.

Centripetal force F_c = mv^2/r = m*r*omega^2, directed toward the centre of the circular path; it is the net force that keeps a body moving in a circle.