Physics Test-38

The dimension of frequency \(=[T]^{-1}\)

Now we check all options

\(\left[\frac{L}{R}\right]=[T]\)

\(\left[\frac{R}{L}\right]=\left[T^{-1}\right]\)

\([{RC}]=[{T}]\)

\(\left[\frac{1}{R C}\right]=\left[T^{-1}\right]\)

\(\left[\frac{1}{\sqrt{L C}}\right]=\left[T^{-1}\right]\)

Only \([RCL] \neq\left[T^{-1}\right]\)

When the net external torque acting on a system is zero, the total angular momentum of the system remains constant. Therefore the angular momentum of a moving body remains constant if net external torque is not applied.

The entropy of an isolated system continuously decreases and becomes a minimum at the state of equilibrium.

If an isolated system’s entropy differs from some parameter, then that parameter has a certain value that maximizes the entropy.

Work done can be positive, negative and zero. When a body is being lifted in the upward direction, the force of gravity is acting in the downward direction. But, the displacement of the body is in the upward direction. Since the angle between the force and displacement is \(180^{\circ}\), the work done by the gravitational force on the body is negative. Diagrammatic representation is given.

As we know,

\(\mathrm{F=\frac{G m_1 m_2}{R^2}}\)

Since, \(\mathrm{G}\) is the universal gravitational constant, its value will remain constant throughout the universe.

We know that the mass of body remains same on Earth and the moon.

Therefore there will be no change in the value of \(\mathrm{m_1}\) and \(\mathrm{m_2}\)

As the masses are placed at distance \(\mathrm{R}\) and there is no difference in the distance on the moon, it will remain same.

Therefore, as \(\mathrm{G, m_1, m_2}\) and \(\mathrm{R}\) remain same both on Earth and the moon, the ratio of force of gravitation will be \(1: 1\)

A hydraulic ram is a pump that lifts water without any external power for its operation.

An essential requirement for the satisfactory operation of hydraulic rams is the availability of large amounts of water with a small positive head or height. Such a large amount of water at a low altitude is sufficient to lift a small amount of water to a higher height. The hydraulic system works on the principle of Pascal's law which states that the pressure in an enclosed liquid is the same in all directions.

Given,

Diameter of the sphere \(=2.4\)

\(\therefore\) Radius of sphere, \(r=\frac{2.4}{2}=1.2 {~m}\)

Surface charge density of conducting sphere, \(\sigma=80 \times 10^{-6} {C} / {m}^{2}\)

Therefore,

Charge on sphere will be:

\(q=\sigma A=\sigma 4 \pi r^{2}\)

\(q=80 \times 10^{-6} \times 4 \times 3.14 \times(1.2)^{2}\)

\(q=1.45 \times 10^{-3} {C}\)

Then, the total electric flux leaving the surface of the sphere will be calculated using the gauss formula, i.e.,

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

\(\phi=\frac{1.45 \times 10^{-3}}{8.854 \times 10^{-12}} \quad\)\( (\because \epsilon_{0}=8.854 \times 10^{-12}) \)

\(\phi=1.6 \times 10^{8} {Nm}^{2} / {C}\)

Iron objects can be protected by electroplating them withchromium,nickel and zinc.

Metals can be protected against corrosion by electroplating them with less reactive metals on their surface. For example, iron is protected against corrosion by electroplating chromium, nickel and zinc on its surface.

The intrinsic impedance of the wave is defined as the ratio of the electric field and the magnetic field phasor (complex amplitude), i.e.

\(\eta=\frac{E}{H}\)

For free-space, the intrinsic impedance is a real quantity, i.e.

\(\eta=\eta_0=120 \pi\)

Analysis:

\(E=E_{\max } \sin (K x-\omega t)\)

With \(\mathrm{E}_{\max }=100 \mathrm{~N} / \mathrm{C}\), the magnetic field will be:

With \(\eta=\frac{E}{H}\):

\(H=\frac{E}{\eta} \)

\(H=\frac{100}{120 \pi} A / m \)

\(B=\mu_0 H \)

\(B=4 \pi \times 10^{-7} \times \frac{100}{120 \pi} \)

\(B=3.33 \times 10^{-7} \mathrm{~T}\)

In semiconductors, both electrons and holes are charge carriers and will take part in conduction.

In \(n\)-type semiconductors they are electrons, while in \(p\)-type semiconductors they are holes. The less abundant charge carriers are called minority carriers in \(n\)-type semiconductors they are holes, while in \(p\)-type semiconductors they are electrons.