Formulae

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Here are the formulae from Physics, chemistry and Biology. These are very important for entry test preparation also for FSc exams.

Physics

v = u + at
v² = u² + 2as
s = ut + ½at²

F = ma

F = Gm₁m₂/r²

a = v²/r

Static friction = F_N m_S

Dynamic friction = F_N m_D

MA = load/effort = number of supporting ropes in a frictionless pulley system

VR = distance moved by effort / distance moved by load = number of supporting ropes

Efficiency = work out / work in

Moment = F x perpendicular distance to pivot point

Momentum = mv

Smv before collision = Smv after collision

Impulse = Ft

PE = mgh

KE = ½mv²

Work done = Fd

Power = Fd/t

Dl = kF

Y = stress / strain = (F/A) / (Dl/l)

S = stress / strain = (perpendicular F/A) / (Dx/l)

B = stress / strain = DP / (DV/V)

f µ Ö (k/m)

T = 2p Ö (l/g)

r = m/V

Upward force on a body = weight of fluid displaced by that body

Hydrostatic pressure = rgh

r₁A₁v₁ = r₂A₂v₂

P₁ + rgh₁ + ½rv₁² = P₂ + rgh₂ + ½rv₂²

Velocity of sound in a fluid, v = Ö (B/r)

v µ Ö (T/mw)

Velocity of sound in a solid = Ö (Y/r)

Velocity of a wave in a taut string = Ö (tension/[mass/length])

dB = 10log₁₀(I/10^-12)

Beat frequency = difference between the two frequencies

f' = f(C±Vd / C±Vs)

F = kq₁q₂/r²

E = F/q

Between two parallel plates, E = V/d
Concerning a point charge, E = kq/r²

V = Fd/q

V = IR

For resistors in series, R_T = R₁ + R₂ + R₃ + ...

For resistors in parallel, 1/R_T = 1/R₁ + 1/R₂ + 1/R₃ + ...

Resistivity = RA/l

C = q/V = permitivity x A/d

For capacitors in series, 1/C_T = 1/C₁ + 1/C₂ + 1/C₃ + ...

For capacitors in parallel, C_T = C₁ + C₂ + C₃ + ...

P = IV

If a.c., P = (I_max/Ö2) (V_max/Ö2) = I_max V_max/2

n₁sin i = n₂sin r

1/f = 1/u + 1/v

Lens power = 1/f where f is the focal length in m. Lens power is measured in diopters.

Two lenses in contact: 1/F = 1/f₁ + 1/f₂

E = hf

A_t = A_oe^-kt

t½ = ln2/k

Chemistry

Number of moles = mass in grams / molecular weight

PV = nRT

KE µ T

v µ Ö(T/mw)

P_T = P₁ + P₂ + P₃ + ...

P = mole fraction of solvent x Po

DP = mole fraction of solute x Po

DT_BP = k_b (molality of solute particles)

DT_FP = -k_f (molality of solute particles)

Osmotic Pressure = RT [molarity of solute particles]

pH = -log₁₀[H⁺]

pOH = -log₁₀[OH^-]

K_w = [H⁺] [OH^-] = 10^-14 (at 25^oC)

K_a = [H⁺] [A^-] / [HA]

pK_a = -log₁₀K_a

K_b = [HA] [OH^-] / [A^-]

pK_b = -log₁₀K_b

K_a K_b = 10^-14

pK_a + pK_b = pK_w = 14

pH = pK_a + log₁₀[A^-]/[HA]

DE = q - w

DG = DH - TDS

DG = DG° + RTlnQ

K_eq = e^DG°/-RT

Reaction Order	dA/dt	Integrated Forms
0	dA/dt = k	At = A0 - kt
1	dA/dt = kA	At = A0e-kt
2	dA/dt = kA2	1/At = (1/A0) + kt

E = E° - (RT/nF)lnQ = E° - (0.026/n)lnQ

K_eq = e^nFE°/RT

DG° = -nFE°

Biology

p² + 2pq + q² = 1