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Calculation:

The volume of liquid displaced by floating ice is given by

\(V_D = \frac{M} {\sigma_l}\)

The volume of water formed by melting ice,

\(V_F = \frac{M} {\sigma_W}\)

If \(\sigma_l > \sigma_W, then, \frac{M} {\sigma_L} < \frac{M} {\sigma_W}\)  i.e \(V_D < V_F\)

Therefore,

Volume of liquid displaced by floating ice will be lesser than water formed and so the level of liquid will rise.

Correct option-2

Concept:

In a communication system, the electromagnetic waves transmitted by the transmitter travels in three different modes to reach the receiver according to its frequency range.

1. Ground wave propagation or surface wave propagation (nearly 2 kHz to 2 MHZ) 2. Sky-wave propagation or ionospheric propagation (nearly 3 MHZ to 30 MHZ) 3. Space wave propagation (nearly 30 MHZ to 400 MHZ)

1. Ground wave propagation:

• If the electromagnetic waves transmitted by the transmitter antenna over the surface of the earth reach the receiver, then the propagation is called ground wave propagation.
• In this mode of transmitting and receiving antennas must be close to the earth's surface.
• During effective transmission through ground wave propagation mobe, electrical signals are attenuated over a distance.

2. Sky-wave propagation:

• In the sky-wave propagation, the electromagnetic wave is radiated from the antenna, directed upwards at large angles gets reflected by the ionosphere back to the earth.
• The frequency range of EM waves in this mode of propagation is 3 to 30 MHZ.
• It is used for short-wave broadcast services medium and high frequencies are for long-distance radio communication.

3. Space wave propagation: 

• The process of sending and receiving information signals through space is called space wave communication.
• The EM waves above 30 MHZ frequency traveling from the transmitter to receiver in a straight line are used for line of sight communication (LOS).

Explanation:

• If we wish to send radio signals at far stations then we must believe in skywave propagation.
• In any sky-wave propagation, we broadcast the radio signal over a long distance by the reflection of signals from the ionosphere.
• Actually, the ionosphere acts as a rare medium whose refractive index is less than the free space value.
• When the radio wave specific frequency send to the ionospheric layer, the bending of the beam reaches at some critical angle, after that, it will be reflected back.
• This phenomenon is also called ionospheric TIR (total internal reflection).

Hence, option-2 is correct.

• EM waves of frequency above 30 MHZ can easily penetrate through the ionosphere and do not undergo reflection.
• Extremely long-distance communication is also possible as radio waves can undergo multiple reflections between the earth and ionosphere.
• A single reflection helps the radio waves to travel about 4000km.
• The charged ions of the ionosphere provide a reflecting medium for reflection of radio waves or communication waves back to the earth's surface within the permitted frequency range.
• This phenomenon is called the total internal reflection of the EM wave.

CONCEPT:

• Measurement of any physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard called unit, and a Dimension is a mathematical tool used for studying the nature of physical quantities.
• The basic concept of dimensions is that we can add or subtract only those quantities which have the same dimensions.
• And the dimensional formula is defined as the expression of the physical quantity in terms of mass, length, and time.

​EXPLANATION:

Strain:

• The ratio of change in configuration to the original configuration is called strain.
• As the strain is the ratio of two like quantities, it has no units and no dimensions.
• and has no dimension.
• Its dimension can be expressed as M0L0T0.

​The correct answer is M0L0T0​.   

CONCEPT:

• The measurement of the effect of electric field on the motion of electrons is called mobility of electrons.
• Mobility of electrons is equal to drift velocity per unit electric field.

Mobility (μ) of free electrons is given by:

\(\mu =\frac{e~\tau }{m}\)

Where e is charge on an electron, m is mass of an electron and τ is relaxation time.

EXPLANATION

• According to the given formula for the mobility of free electrons, it is directly proportional to the relaxation time. So option 2 is correct.
• The mobility of free electrons varies sometimes directly proportional to electron density and sometimes it varies inversely proportional to electron density. So options 1 and 3 are wrong.

option(1)

CONCEPT:

• Dyne: It is those centimeter-gram-second system units that represent the Force.

EXPLANATION:

• Dyne: It is the unit of force in the centimeter-gram-second system of physical units, is equal to the force.

1 dyne equals =  0.00001 newtons.

or 1 N = 100000 dyne 

Additional Information

• Force: It is those vector quantity that is a vector product of mass and acceleration.

Force = mass × acceleration

• Energy: It is that physical quantity that is defined as the capacity to doing work.

Energy = Power × Time, the S.I unit of power is Watt.

• Work: It is that physical quantity that is a product of Force and displacement

Work = Force× displacement, The SI unit of work is Jule

CONCEPT:

• Compound Microscope: A compound microscope is a high magnification microscope that uses a compound lens system to obtain a bigger image of small objects.
• A compound microscope has multiple lenses: the objective lens is compounded (multiplied) by the eyepiece lens to obtain a high magnification.
• Higher magnification is achieved by using two lenses rather than just a single magnifying lens.

The total magnification of a compound microscope: 

M = moMe

\(M=\frac{L}{f_o}\times\frac{D}{f_e}\)

where L is the tube length, fo is objective focal length, fe is eyepiece focal length, and D is shortest distance Point D = 25 cm

EXPLANATION:

• The total magnification of a compound microscope is

\(M=\frac{L}{f_o}\times\frac{D}{f_e}\)

• M will increase if f_o and f_e are small.
• For having the large magnification power of a compound microscope, the focal lengths of the objective lens and eye-piece should be small.
• So the correct answer is option 3.

CONCEPT:

Law of equipartition of energy:

• According to the law of equipartition of energy, for any dynamic system in thermal equilibrium, the total energy for the system is equally divided among the degree of freedom with each degree of freedom having average energy equal to \(\frac{1}{2}k_BT\).

Where kB = Boltzmann constant and T = absolute temperature

• If a molecule is constrained to move along a line then it has one degree of freedom.
• If a molecule is constrained to move in a plane then it has two degrees of freedom.
• If a molecule is free to move in space then it has three degrees of freedom.
• Molecules of a monatomic gas like argon have only translational degrees of freedom.
• Molecule of diatomic gas such as O2 and N2 has three translational degrees of freedom. But in addition, it has also two independent axes of rotation. The molecule thus has two rotational degrees of freedom, each of which contributes a term to the total energy consisting of translational energy and rotational energy
• Molecules like CO even at moderate temperatures have a mode of vibration, i.e. its atoms oscillate along the interatomic axis like a one-dimensional oscillator, and contribute a vibrational energy term to the total energy.
• While each translational and rotational degree of freedom has contributed only one ‘squared term’ but one vibrational mode contributes two ‘squared terms’: kinetic and potential energies.

EXPLANATION:

• We know that if a molecule is free to move in space then it has three degrees of freedom. Hence, option 3 is correct.

CONCEPT:

• Momentum: A property of a body in motion that is equal to the product of the body's mass and velocity is called momentum.

P = mv

where P is the momentum of the body, m is the mass of the body, and v is the velocity of the body.

• Newton's Second Law of Motion: It says that the net external force on a system or body is equal to the change in momentum of the system or body divided by the time over which it changes.

Mathematically:

\(F_{ext} = {Δ p \over Δ t}\)

where Fext is the external force on the system, Δp is the change in momentum, and Δt is the change in time.

EXPLANATION:

Newton's second law of motion in momentum form can be written as:

\(F_{ext} = {Δ p \over Δ t}\)

which says the rate of change of momentum \( {Δ p \over Δ t}\) is equal to the external force on a system.

So the correct answer is option 1.

The correct answer is option 2) i.e a torque and a net force

CONCEPT:

• Electric field strength is a measure of the electric field intensity at a point due to a charge. It is the amount of electric force produced per unit charge.
• Electric field strength (E) at a point due to a point charge q is given by the formula

 \(E =\frac{F}{q}\)

Where r is the distance from the point charge to the point at which E is determined.

• Electric dipole a couple formed from two equal opposite charges q and –q, which are separated by a distance 2a.

EXPLANATION:

In a uniform electric field:

• When an electric dipole is placed in a uniform electric field of intensity E, the negative and positive charges experience two forces -qE and +qE respectively.
• These two forces are opposite and hence, the net force the dipole experiences will be zero. However, Since they are separated by a distance, a torque is produced.

In a varying or non-uniform electric field:

• In a varying electric field, the force experienced by the two charges of the dipole will be of different magnitudes, and hence, the dipole will experience a net force.
• Since the charges are separated by a distance, they will experience a torque as before.

Thus, an electric dipole is placed in varying electric field experiences a torque and a net force.

To use Galvanometer as a Voltmeter we must connect a high resistance in series with it, because it must draw a very small current, otherwise the voltage measurement will disturb the original set up by an amount which is very large.