Physics Test-12

The parallax method is used to determine large distances, such as the distance from Earth to a planet or a star. Parallax is the projected shift in the position of one object with respect to another when we move the point observation slant. The distance between two points of observation is called the base \((b)\). The distance of the object from the two points of view is \(D\). The angle between the two directions along which the object is viewed is the parallax angle or displacement angle \((θ)\).  

If \(S\) is the position of the object and \(AB\) is the two points of observation,

\(\theta=\frac{b}{D}\)

The triangulation method finds the angles in a triangle formed by three observation points. The other distances in a triangle are calculated using trigonometry and the measured length of just one side. It is used for geographic measurement and not astronomical distance.

The echo method uses the principle of reflection of sound or light. Knowing the speed of the wave and the time of reflection back to the source, the distance between the two points is calculated. This is not a very accurate method and therefore astronomical distances cannot be relied upon.

Angular momentum, L = I × ω ----(1) ,Roational kinetic energy \(=E=\frac{1}{2} I \omega^2 \Rightarrow \omega=\sqrt{\frac{2 E}{I}}\)----(2)
Substituting equation (2) inequation(1), we get
\(\mathrm{L}=I \times \sqrt{\frac{2 E}{I}}=\sqrt{ (2 \mathrm{EI}) }\)

In physics, the second law of thermodynamics says that heat flows naturally from an object at a higher temperature to an object at a lower temperature, and heat doesn’t flow in the opposite direction of its own.

In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of potential energy include the gravitational potential energy of an object that depends on its mass and its distance from the center of mass of another object, the elastic potential energy of an extended spring, and the electric potential energy of an electric charge in an electric field. The unit for energy in the International System of Units (SI) is the joule, which has the symbol J.

And when the water is flowing or falling in the dam the energy is known as kinetic energy.

According to keplars law: The square of time period of revolution of the planet is proportional to the cube of semi major axis of the ellipse traced by the planet.

\(T^{2} \propto\) \(a^{3}\)

This equation is modified to:

\(T^{2}=\frac{2 \pi a^{3}}{G M}\)

\(\mathrm{T}=\) Time period of the satellite

\(\mathrm{a}=\) semi-major axis

\(\mathrm{G}=\) gravitational constant

\(\mathrm{M}=\) mass of the earth (in this case)

Here, \(\frac{2 \pi}{G M}\) is the constant of proportionality.

So: \(T=\frac{\sqrt {2 \pi}}{\sqrt{GM}}a^{\frac{3}{2}}\).....(1)

Now, we know the semi-major axis of an elliptical path is the arithmetic mean of the minimum and the maximum distance covered by the planet.

Therefore, in this case:

\(r_{1}=\) Minimum distance covered

\(r_{2}=\) Maximum distance covered

So,

\(a=\frac{r_{1}+r_{2}}{2}\)

Put this value in (1).

\(T=\frac{\sqrt {2 \pi}}{\sqrt{GM}} \left( \frac{r_{1} +r_{2}}{2} \right)^{\frac{3}{2}}\)

Thus, this is the value of the time period of the satellite.

A body just floats in seawater but sinks in river water because seawater has greater density than river water.

• Seawater is denser than river water due to the addition of salt.
• The density of a substance is defined as the mass per unit volume. This means that the upthrust of seawater on the body is greater than the weight of the body. So it floats while the upthrust of the river water on the body is lesser than the weight of the body so it sinks.
• The viscosity of seawater is higher than that of freshwater because of its higher salinity.

Let us assume that the charge \(q=\pm 10 \mu C=10^{-5} C\) is placed at a distance of \(5 cm\) from the square \(A B C D\) of each side \(10 cm\). The square \(A B C D\) can be considered as one of the six faces of a cubic Gaussian surface of each side \(10 cm\).

Now, the total electric flux through the faces of the cube as per the Gaussian theorem:

\(\phi=\frac{q}{\epsilon_{0}}\)

Therefore, the total electric flux through the square \(ABCD\) will be:

\(\phi_{E}=\frac{1}{6} \times \phi\)

\(=\frac{1}{6} \times \frac{q}{\epsilon_{0}}\)

\(=\frac{1}{6} \times \frac{10^{-5}}{8.854 \times 10^{-12}} \quad\left(\because \epsilon_{0}=8.854 \times 10^{-12}\right)\)

\(=1.88 \times 10^{5} Nm ^{2} C ^{-1}\)

Chromium plating is done on many objects like car parts, wheel rims, and bath taps because the chromium layer can be decorative, provide corrosion resistance, ease cleaning procedures, or increase surface hardness.

Velocity of electromagnetic waves in a medium depends upon electrical and magnetic properties of the medium.

Velocity of an electromagnetic wave:

The velocity of an electromagnetic wave in a medium can be written as:

• \(v=\frac{1}{\sqrt{\mu \varepsilon}}\) Where, \(\mu\) is the permeability of the medium and \(\varepsilon\) is the permittivity of the medium.
• The permeability of a medium is a measure of how much a medium can be magnetized with an external magnetic field.
• The permittivity of a medium is a measure of how much a medium can be electrically polarized with an external electric field.
• Thus, the velocity of an electromagnetic wave in a medium depends both on the magnetic and electrical properties of the medium.

Semiconductors have negative temperature co-efficient. The reason for this is, when the temperature is increased, a large number of charge carriers are produced due to the breaking of covalent bonds and hence these electrons move freely and gives rise to conductivity.