The antrodes is not exactly formed at the open end, but a small distance above be open end.
This is called and correction. To computer the end correction,
L₁ + e = \(\frac{\lambda}{4}\) and L₂ + e = \(\frac{3}{4}\lambda\)

(i) When any object is heated, it receives heat from the source of heat. Once the object is taken from the heated source, the object has more internal energy than before.
(ii) Heat is the energy in Uansit and which flows from an object at higher temperature to an object at lower temperature. Heat is not a quantity. So the statement is wrong, instead An object is hot will be appropriate.

1. Law of orbits
Each planet moves around the Sun in an elliptical orbit with the Sun at one of the foci.
2. Law of area
The radial vector (line joining the Sun to a planet) sweeps equal areas in equal intervals of time.
3. Law of period
The square of the time period of revolution of a planet around the Sun in its elliptical orbit is directly proportional to the cube of the semi major axis of the ellipse. It can be written as :
\(T^{2} \propto a^{3}  \)
\(\frac{T^{2}}{a^{3}}=\text { constant. }\)

We use Newton's second law, \(\vec { F_{ net } } =m\vec { a } \) where \({ \vec { F } }_{ net }=\vec { { F }_{ 1 } } +\vec { { F }_{ 2 } } \). From the above equations the acceleration is \(\vec { a } =\frac { \vec { { F }_{ net } } }{ m } \), where
\(\vec { { F }_{ net } } =(5+3)\hat { i } +(8-4)\hat { j } +(7+3)\hat { k } \)
\({ \vec { F } }_{ net }=8\hat { i } +4\hat { j } +10\hat { k } \)
\(\vec { a } =\left( \frac { 8 }{ 2 } \right) \hat { i } +\left( \frac { 4 }{ 2 } \right) \hat { j } +\left( \frac { 10 }{ 2 } \right) \hat { k } \)
\(\vec { a } =4\hat { i } +2\hat { j } +5\hat { k } \).

Force \(\vec F=\vec i+2\vec j+3\vec k\)
Distance \(\vec S=4\vec i+6\vec j\)
Work done  \(\vec F.\vec S=(\vec i2\vec j+3\vec k).(4\vec i+6\vec j)=4+12+0=16J\)

Meter scale is longer and larger than a match stick. Meter scale's centre of gravity is higher but match stick has centre of gravity much lower as compared to scale. Higher the centre of gravity easier it is to balance.

When the oscillator is allowed to oscillate by displacing its position from equilibrium position, it oscillates with a frequency which is equal to the natural frequency of the oscillator. Such an oscillation or vibration is known as free oscillation or free vibration.

Relation between the average kinetic energy and pressure is
\(\mathrm{P}=P=\frac{2}{3} K . E\)
P - Pressure
K.E - kinetic energy

Let length of rod be l
Let mass of rod be M
∴ Moment of inertia of the uniform rod about an axis passing through its centre and perpendictrlar to an axis of the rod
\(I=\cfrac { Ml^{ 2 } }{ 12 } \)........... (1)
When rod is heated by temperature \(\triangle \)T, there is increase in length of rod is
\(\triangle l=l\alpha _{ L }\triangle T\)   ........(2)
\(\alpha _{ L }\) - coefficient of linear expression
Now moment of inertia \({ I }^{ ' }=\cfrac { M }{ 12 } \left( 1+\triangle l \right) ^{ 2 }\)
\(I'= \cfrac { M }{ 12 } \left( 1+l{ \alpha }_{ L }\triangle T \right) ^{ 2 }\)
By substituting \(\triangle l\) from the equation (2)
\({ I }^{ ' }=\cfrac { { Ml }^{ 2 } }{ 12 } \left( 1+{ \alpha }_{ L }\triangle T \right) ^{ 2 }\)
\({ I }^{ ' }=\left( l+{ \alpha }_{ L }\triangle T \right) ^{ 2 }\) 

Reynold's number is a dimensionless number. It is used to find the nature of the flow of fluid, whether it is streamlined or turbulent.
Reynold's number \(R_{e}=\frac{\rho v D}{\eta }\)
ρ - denotes the density of the fluid v - denotes the velocity of the fluid
D - denotes the diameter of the pipe
η - denotes the coefficient of viscosity the fluid