JEE Physics Important Formulas Part -5

Linear Momentum Formula

The formula for linear momentum are as stated below

Description 

Formula

Linear Momentum

p=mv

p is linear momentum, m is mass and v is velocity

Conservation of momentum

m₁u₁+m₂u₂=m₁v₁+m₂v₂

Where

P = Momentum,

m = Mass and

u,v= velocity

Elastic Collision

m₁v_1i+m₂v_2i=m₁v_1f+m₂v_2f

Where i = initial and f = final

Inelastic collision

m₁v_1i+m₂v_2i=(m₁+m₂₎v_2f

Force (from Newton’s second law)

F=m×a

F_net=dp/dt

Momentum in terms of kinetic energy

p=mv

p²=m²v²

p²=2m(1/2mv²)

p²=2mK

Here, K = kinetic energy

Dimensional Formula of Momentum

[M¹L¹T^-1]

Geometrical Optics Formula

The formula for geometrical optics are as stated below

Description

Formula

Laws of Reflection of light

The incident ray, refracted ray, and normal always lie on the same plane.

Snell’s law

According to the Snell’s law

sin i/sin r = constant

Here,

i = angle of incidence

r = angle of reflection

Relative refractive index

The Relative refractive index is given as

n= c/v

here,

n = refractive index

c = speed of light in vacuum

v = speed of light in medium

Lateral Shift

Lateral Shift is given as

lateral shift = t.sin (i-r)/cos r

Normal shift on a single surface

The normal shift on a single surface is given as

Normal shift = t.(1-1/n)

Relation between refractive index and critical angle

The relation between refractive index and critical angle is given as

n = 1/sin c

Refraction through a prism

The refractive index of a prism is given as

n\ =\ \frac{sin\left(a+\frac{\delta}{2}\right)}{sin\ \frac{A}{2}}

Lens maker formula for thin lenses

Lens maker formula for thin lenses is given as

Power of lens

Power of lens is given as

P=1/f

Equivalent focal length of combination of two thin lenses

1/f=1/f₁+1/f₂

Heat And Thermodynamics Formula

The formula for heat and thermodynamics are as stated below

Description

Formulas

Kirchhoff’s Law

Emissive power of body/Absorptive power of body= Emissive power of black body

Conduction

Rate of flow of heat in conduction is determined as

dQ/dt=-KA.dT/dx

• K = thermal conductivity

• A = area of cross-section

• dx = thickness

• dT = temperature difference

Newton’s law of cooling

dθ/dt =(θ-θ₀)

• Here,

• θ and 0 = temperature corresponding to object and surroundings.

Temperature scales

F=32+9/5×C

K = C +273.16

• F = Fahrenheit scale

• C = Celsius scale

• K = Kelvin scale

Ideal Gas equation

PV= nRT

• Here,

• n = number of moles

• P = pressure

• V = Volume

• T = Temperature

Van der Waals equation

(p+a(n/V)²)(V-nb) = nRT

• a(n/V)² = correction factor for intermolecular forces

• nb = correction factor for molecule size

• n = number of moles

• T = Temperature

• V = Volume

• p = pressure

Thermal expansion

Linear Expansion

L= L₀(1+α∆T)

Area Expansion

A= A₀(1+β∆T)

Volume Expansion

V= V(1+γ∆T)

Relation between α, β and γ for the isotropic solid

α/1=β/2=γ/3

Stefan- Boltzmann’s law

u = σAT⁴ (Perfect black body)

u = eσAT⁴ (Not a perfect black body)

• here,

• = Stefan’s constant = 5.67×10^-8 watt / m²K⁴

• u/A = energy flux

• e = emissivity

Thermal resistance to conduction

Thermal resistance is given as

R=L/KA

• K = material’s conductivity

• L = plane thickness

• A = plane area

Hooke’s Law Formula

The formula for Hooke’s law  are as stated below

Description

Formula

Formula for Hooke’s Law

F=-kx

Where F = force, k = constant and x = displacement

Note: Hooke’s law can be expressed in the form of stress and strain.

According to Hooke’s law

Stress ∝ Strain

That is,

Stress =K×Strain

Where K is the proportionality constant

Formula for Stress

Stress (σ)=F/A

Where,

F is the restoring force, and

A is the cross-section area

Formula for Strain

Strain (ε) =ΔL/L

Where,

ΔL= Change in length and

L = original length

SI unit of Stress

N/m²

Young’s Modulus (Y)

Y=Tensile stressTensile Strain

Y=F_l/A÷∆l/l

Shear Modulus

Y=Shearing stressShearing Strain

Y=F_l/A÷∆x/h

Inductance Formula

The formula for inductance are as stated below

Description

Formula

Inductance

𝐿=𝜇N²𝐴/𝑙

Where

𝐿 – inductance in Henry(H)

𝜇 – permeability (Wb/A.m)

𝑁 – number of turns in the coil

𝐴 – area encircled by the coil

𝑙 -length of coil(m)

Induced voltage in a coil (V)

The voltage induced in a coil (V) with an inductance of L is given by

𝑉=𝐿 𝑑𝑖/𝑑𝑡

Where,

𝑉 = voltage(volts)

𝐿 – inductance value(H)

𝑖 -the current is(A)

𝑡 -time taken (s)

Reactance of inductance

The reactance of inductance is given by:

𝑋=2𝜋𝑓𝐿

Where,

Reactance is 𝑋 in ohm

The frequency if 𝑓 in Hz

Inductance is 𝐿 in Henry(H)

Magnetic Flux

The magnetic flux through a plane of area dA placed in a uniform magnetic field B is given as

When the surface is closed, then magnetic flux will be zero. This is due to magnetic lines of force are closed lines and free magnetic poles is not exist

Induced Current

Induced Current is given as

I=E/R = N/R(dϕ/dt)= N/R(ϕ₁– ϕ₂)

Mutual – Induction

Mutual – Induction is given as

e₂=d(N₂ϕ₂/dt = M.dl₁/dt

Therefore,

M=μ₀N₁N₂A/l