Chapter #1- Uncertainty
π₯ =π΄+π΅
π₯ =π΄−π΅
π₯ =π΄×π΅
π₯=
}
}
π₯=π΄
π₯ = ππππ π‘. π΄
πΏπ₯ = πΏπ΄ + πΏπ΅
πΏπ₯ πΏπ΄ πΏπ΅
=
+
π₯
π΄
π΅
}
πΏπ₯
πΏπ΄
= π΅.
π₯
π΄
βπ₯ = π₯ − π₯
Vectors:
π=
π +π
πππ π =
π
π
π = π πππ π
π ππ π =
d
π
π
π = π π ππ π
dy
θ
πππ
π ππ π =
βπ¦π
dx
πππ
πππ π =
βπ¦π
π‘ππ π =
πππ
πππ
Chapter #2- Kinematics
β
π=β
a=acceleration; v= velocity; t=time
π=
v= final velocity; u= initial velocity
π£ = π’ + ππ‘
π = π£π‘
π£
=
s= displacement
π’+π£
2
π = π’π‘ + 1 2 ππ‘
For flight time from rest:
π‘ =
g=acceleration of free fall; h=height of fall; t=time
πΎπΈ = πΎπΈ + ππππ ππ πΎπΈ
πΊπππ ππ πΎπΈ = πΎπΈ − πΎπΈ
πΎπΈ = 1 2 ππ£
βπΎπΈ = 1 2 π(π£ − π£ )
βππΈ = βπΎπΈ with no external force, friction
ππΈ = ππβ
βππΈ = ππ(β − β )
Momentum:
π = ππ£
P=momentum; m=mass-kg; v=velocity
βπ = π. βπ£
βπ
βπ£
= π.
βπ‘
βπ‘
βπ
= π. π
βπ‘
πΉ = ππ
β
πΉ=β
2nd law of motion
βπ = πΉ × βπ‘
βP= impulse of force
π = ππ£
π = (ππ£)
π = π .π£
π = π. π. π£
π
= ππ£
π
π
1
= ππ£
2π 2
π
= πΎπΈ
2π
π = √2ππΎπΈ
Law of conservation of momentum
πΉ = −πΉ
βπ
βπ
=−
βπ‘
βπ‘
(π − π ) = −(π − π )
π π’ − π π’ = −π π£ + π π£
ππππππ‘π’π ππ π π¦π π‘ππ ππππππ ππππππ πππ = ππππππ‘π’π ππ π π¦π π‘ππ πππ‘ππ ππππππ πππ
π π’ − π π’ = (π + π )π for if the bodies stick together after collision
for a perfectly elastic collision
π’ +π’ =π£ +π£
πΉ = ππ΄π£
F=force of flow of fluid; p=density; A=cross-sectional area; v=velocity
πΉ = ππ΄π£
FR = flow rate (kg s-1 );
π = ππ΄π£π‘
m=mass of fluid; t= time taken for ’m’ to flow
Chapter#3- Work, energy and Power
W=work; f=force; d=distance in direction of force
π = π×π
π = ππ πππ π for an inclined plane
P=pressure; V=volume
π = π(π − π )
π = ππ
π = ππ΄π
π = π × π΄π₯
π = π × βπ
π = π(π − π )
Wf=work against friction
πΊππΈ − πΎπΈ = π
πΈπππππππππ¦ =
π=
ππ’π‘ππ’π‘ πππ€ππ
× 100%
ππππ’π‘ πππ€ππ
P=Power; W=work; t=time
F=force; v=velocity
π = πΉπ£
Chapter #4-Forces, density and pressure
π=
P=pressure; f=force; a= surface area
π = ππβ for liquids
Po=atmospheric pressure
π = π + ππβ
πΉ = πππ
F=upthrust; V=volume of liquid displaced; p=density of liquid
π =πΉ×π
T=moment of force; F=force; l=length from pivot
π = πΉ × π πππ π
π=πΉ×
F
R
F
π
2
F
θ
F
π = πΉ × 2π
l
π=
π
π£
P=density; m=mass; v=volume
F
Chapter#5- Deformation of solids
F=force/load; k=spring constant; x=extension
π=
πΉ = ππ₯
ππ‘ππππ ππππππ¦ = 1 2 πΉπ₯
ππ‘ππππ ππππππ¦ = 1 2 ππ₯
π=
σ=stress; F=force/load; A=cross-sectional area
π=
ε=strain; e=extension; l=length of spring
πΈ=
E=Young’s modulus
πΈ=
πΉπ
ππ΄
Chapter#6-Electricity
I=current; Q=Charge; t=time
πΌ=
π = πΌπ‘
ππ. ππ π π πππ π ππ =
π = ππ
=π
Q=Amount of charge on object; n=integer; e=elementary charge
N=Total no. of π π πππ π ππ; no. of π π πππ π’πππ‘ π£πππ’ππ; π = π£πππ’ππ
I=current; A=cross-sectional area of wire; q=elementary charge; n=no. of
π π πππ π’πππ‘ π£πππ’ππ; V=volume
πΌ = ππ΄ππ
R=resistance; ρ=resistivity; l=length; A=cross sectional area
π
=
π=
ππ’πππππ‘
πππππππ‘πππ¦ πβππππ
π
π΄
π
W=energy consumed; V=voltage; Q=transferred charge
π=
π = ππ
π = πΌπ
πΌ=
π
π
π
=
π
πΌ
π =π +π
V=voltage; I=current; R=resistance
energy conservation principle; Kirchoff’s 2nd law
πΌ π
=πΌ π
+πΌ π
π
=π
+π
for series only
π
π
=
π
π
πΌ=
π
π
+π
π =
π
×π
π
+π
π =
π
×π
π
+π
πΌ =πΌ +πΌ
=
+
π
=
π
π
π
+π
Principle of Kirchoff’s charge; 1st law of conservation
for parallel only
πΌ =
πΌ
×π
π
+π
πΌ =
πΌ
×π
π
+π
π = ππΌ
π=πΌ π
π=
P=power; V=voltage; I=current; R=resistance
π
π
π = πΈ − πΌπ
π = πΈ + πΌπ
battery being used up
battery being charged
null method
=
Chapter #7- Waves and superposition
π£ = πλ
v=speed of wave; f=frequency of wave; λ=wavelength
π=
T=time period for one oscillation
πΌ=
I=intensity of wave; P=power; A=cross sectional area
πΌ∝π΄
A=Amplitude
πΌ
πΌ
=
π΄
π΄
Doppler effect:
π =π
π£
π£+π£
πππ π€βππ π ππ’πππ ππ πππ£πππ ππ€ππ¦ ππππ πππ πππ£ππ
π =π
π£
π£−π£
πππ π€βππ π ππ’πππ ππ πππ£πππ π‘ππ€ππππ πππ πππ£ππ
π = πππ πππ£ππ πππππ’ππππ¦
π = π ππ’πππ πππππ’ππππ¦
v=speed of sound
π£ = π ππππ ππ π ππ’πππ
πππ‘β ππππππππππ = πλ
for constructive interference
πππ‘β ππππππππππ = (π + 1 2)λ
for destructive interference
a=slit separation; λ=wavelength; x=fringe separation; D=distance between slits
and screen
π=
d=distance between consecutive slits; θ=angle of nth order from central
maxima; n=order of maxima
π sin π = πλ
d=distance between consecutive slits; N=Number of slits per metre
π=
π = 2(π − π )
π =length of tube for second harmonic
π =length of tube for first harmonic
π£ = 2π(π − π )
v=speed of wave; f=frequency
Chapter #8-Radioactivity
π→
π + π»π
alpha decay
π→
π+
beta decay
π
gamma decay
π → π+πΎ
π→ π+
π+αΏ‘
π½ − πππππ¦
π→ π+
π+π£
π½ + πππππ¦