DPT Admission Test Physics Syllabus

What is a couple, and what is its moment?

A couple is two equal, opposite, parallel forces with different lines of action. Its moment (torque) = one force x perpendicular distance between them, and it produces pure rotation.

State the two conditions of equilibrium.

First condition: net force is zero (sum Fx = 0 and sum Fy = 0); Second condition: net torque about any point is zero (sum tau = 0).

Differentiate between stable, unstable, and neutral equilibrium.

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

Distinguish between distance and displacement.

Distance is the total path length travelled (scalar, always positive); displacement is the straight-line change in position from start to end with direction (vector).

Differentiate average velocity from instantaneous velocity.

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

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 = initial velocity, v = final velocity, a = acceleration, t = time, s = displacement.

For a body in free fall (ignoring air resistance), what determines its acceleration?

It falls with acceleration g (about 9.8 m/s^2) directed downward, independent of mass; all bodies fall at the same rate in a vacuum.

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 as an equation.

The net force equals the rate of change of momentum; for constant mass, F = ma (force in newtons, mass in kg, acceleration in m/s^2).

State Newton's third law of motion.

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

Define linear momentum and give its formula and SI unit.

Momentum is the product of mass and velocity: p = mv. It is a vector; SI unit is kg.m/s (or N.s).

Define impulse and state the impulse-momentum theorem.

Impulse = force x time of action (J = F.t). The impulse-momentum theorem states impulse equals the change in momentum: F.t = mv - mu.

State the law of conservation of linear momentum.

In the absence of a net external force, the total momentum of a system remains constant; total momentum before a collision equals total momentum after.

Differentiate elastic from 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 (some converts to heat/deformation).

Define work and give its formula for a force at an angle.

Work = force x displacement in the direction of force: W = F s cos(theta). SI unit is the joule (J).

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.

Give the formulas for kinetic energy and gravitational potential energy.

Kinetic energy KE = (1/2)mv^2; gravitational potential energy PE = mgh (m = mass, g = gravity, h = height).

State the law of conservation of energy.

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

For a freely falling body, how does the sum of KE and PE behave?

In the absence of friction/air resistance, total mechanical energy (KE + PE) stays constant; as the body falls, PE converts into KE.

Define power and give its formulas.

Power is the rate of doing work: P = W/t = F.v (work per unit time, or force times velocity). SI unit is the watt (W) = J/s.

Define efficiency and give its formula.

Efficiency = (useful output energy or power / total input energy or power) x 100%. It is always less than 100% due to energy losses (e.g. friction, heat).

Define angular displacement and its SI unit.

Angular displacement (theta) is the angle swept by a rotating body about its axis; SI unit is the radian (rad).

Define angular velocity and give its relation to linear velocity.

Angular velocity omega = angular displacement/time (rad/s); linear (tangential) velocity v = r.omega, where r is the radius.

Define angular acceleration and relate it to tangential (linear) acceleration.

Angular acceleration alpha = change in angular velocity/time (rad/s^2); tangential acceleration a = r.alpha.

Give the formula for centripetal acceleration.

Centripetal acceleration a_c = v^2/r = r.omega^2, directed toward the centre of the circular path.

Define centripetal force and give its formula.

Centripetal force is the net inward force keeping a body in circular motion: F_c = mv^2/r = m r omega^2, directed toward the centre.

Define moment of inertia and state what it depends on.

Moment of inertia (I) is the rotational analogue of mass — a body's resistance to angular acceleration. It depends on the body's mass and how that mass is distributed relative to the axis of rotation. SI unit: kg.m^2.

Give the moment of inertia of a solid sphere and a solid disc/cylinder about their central axes.

Solid sphere: I = (2/5)MR^2; solid disc/cylinder about central axis: I = (1/2)MR^2 (M = mass, R = radius).

Define pressure in a fluid and state how it varies with depth.

Pressure P = F/A (force per unit area). In a fluid at rest, pressure increases with depth: P = rho.g.h, where rho is fluid density, g is gravity, h is depth.

State Archimedes' principle and the buoyant force formula.

A body wholly or partly immersed in a fluid experiences an upthrust equal to the weight of the fluid it displaces: F_b = rho_fluid x V_displaced x g.

State Pascal's law.

Pressure applied to an enclosed (confined) fluid is transmitted undiminished and equally to every part of the fluid and to the walls of the container (basis of hydraulic systems).

State Bernoulli's equation for an ideal fluid.

P + (1/2)rho v^2 + rho g h = constant along a streamline, expressing conservation of energy per unit volume (pressure + kinetic + potential terms).

According to Bernoulli's principle, how does fluid speed relate to pressure?

Where the speed of a fluid increases, its pressure decreases (and vice versa), for flow at the same height.

Define viscosity and state its SI unit.

Viscosity is a fluid's internal resistance to flow (friction between fluid layers). Its SI unit is the pascal-second (Pa.s), also N.s/m^2.

Define terminal velocity and state when it occurs.

Terminal velocity is the constant maximum velocity reached by a body falling through a fluid; it occurs when the downward weight is balanced by the upward drag (viscous force) plus buoyancy, so net force and acceleration become zero.

State Stokes' law for the drag force on a small sphere in a fluid.

F = 6.pi.eta.r.v, where eta is the fluid viscosity, r is the sphere's radius, and v is its velocity.