for isothermal process work done is nrtln(initial volume /final volume) .take r=8.314,t=300+273 k,n=3,vol. initial =4,vol final =1 and thencalculate to get answer 8603.6431 joules.

Ans. The Azimuthal Quantum number is a quantum number for an atomic orbital that determines its orbital angular momentum and describes the shape of the orbital. The azimuthal quantum number is the second of a set of quantum numbers which describe the unique quantum state of an electron (the others being the principal quantum number, following spectroscopic notation, the magnetic quantum number, and the spin quantum number). It is also known as the orbital angular momentum quantum number, orbital quantum number or second quantum number, and is symbolized as {tex}\varphi{/tex}

The Magnetic Quantum number, designated by the letter ml,[dubious ] is the third in a set of four quantum numbers (the principal quantum number, the azimuthal quantum number, the magnetic quantum number, and the spin quantum number) which describe the unique quantum state of an electron. The magnetic quantum number distinguishes the orbitals available within a subshell, and is used to calculate the azimuthal component of the orientation of orbital in space. Electrons in a particular subshell (such as s, p, d, or f) are defined by values of {tex}\varphi{/tex}(0, 1, 2, or 3). The value of m can range from {tex}-\varphi \space to \space \varphi{/tex} inclusive of zero.

Stress is same as that of PRESSURE which is force per unit area and thus have dimensions M¹L^-1T^-2 same as that of PRESSURE. 

While STRAIN means the ratio of change in dimension and original dimension. Thus it is a dimension less quantity. 

According to Newton, when sound waves propagate in air, compression and rarefaction are formed. He assumed that the process is very slow and the heat produced during compression is given to surrounding and heat loss during compression is gained from surrounding. So the temperature remains constant and sound waves propagate through an isothermal process.

According to gas law (<a href="https://en.wikipedia.org/wiki/Boyle%27s_law">Boyle's law</a>),

Differentiating above equation, we get

where, B is the bulk modulus of the air.

If B is the bulk modulus of the air, v is velocity and ρ is the density, then, velocity is given by:

This is the required expression for velocity of sound in air.

<a data-ved="0ahUKEwiyooLvt7TSAhVCOY8KHUShB-sQ9QEIHTAA" href="https://www.google.co.in/imgres?imgurl=https://upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Pendulum2secondclock.gif/220px-Pendulum2secondclock.gif&imgrefurl=https://en.wikipedia.org/wiki/Seconds_pendulum&h=132&w=220&tbnid=xXcb3Ti7ty5QPM:&vet=1&tbnh=105&tbnw=176&docid=Fiqrpi0P8wtiiM&usg=__FXiyBXQQAmRJ6W4z2VCBZZy1HS4=&sa=X&ved=0ahUKEwiyooLvt7TSAhVCOY8KHUShB-sQ9QEIHTAA" id="xXcb3Ti7ty5QPM:" jsaction="fire.ivg_o" role="link" tabindex="0" tag="bia"></a>

A seconds pendulum is a pendulum whose period is precisely two seconds; one second for a swing in one direction and one second for the return swing, a frequency of 1/2 Hz. A pendulum is a weight suspended from a pivot so that it can swing freely.

When a pendulum is displaced sideways from its resting equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force combined with the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth. The time for one complete cycle, a left swing and a right swing, is called the period. The period depends on the length of the pendulum, and also to a slight degree on its weight distribution (the moment of inertia about its own center of mass) and the amplitude (width) of the pendulum's swing.

The first law of thermodynamics is a version of the law of conservation of energy which states that the total energy of an isolated system is constant i.e. energy can be transformed from one form to another but cannot be created or destroyed. The first law is often formulated by stating that the change in the internal energy of a closed system is equal to the amount of heat supplied to the system plus the amount of work done by the system on its surroundings. 

Rolling is a type of motion that combines rotation (commonly, of an axially symmetric object) and translation of that object with respect to a surface (either one or the other moves), such that, if ideal conditions exist, the two are in contact with each other without sliding.

Ans. Let Acceleration due to gravity at Height h is g' and Acceleration due to gravity at surface is g. 

\(g' = g - {35g\over 100} = g- {7g \over 20} = {13g\over 20}\)

We know that Acceleration due to gravity at Height h from the Earth Surface is Given By :

\(g' = g ({1 - {2h\over R}}) \space \space \space \space \space \space \space ... (1) \)

Where (R = 6400 Km ) is Radius of Earth

=> \({13g\over 20 }= g({1- {2h\over R})}\)

=> \({13\over 20 }= ({1- {2h\over R})}\)

=> \(1- {13\over 20 }= {2h\over R}\)

=> \({7\over 20 }= {2h\over R} => h = {7R\over40}\)

=> \( h = {7\times 6400\over40} = 1120\space Km\)

Ans. A node is a place of zero amplitude. An antinode is a place of maximum amplitude.
The distance between successive nodes, and successive antinodes, is half a wavelength. \(({\lambda \over 2})\)

If two vectors are considered to be the adjacent sides of a Parallelogram, then the resultant of two vectors is given by the vector which is a diagonal passing through the point of contact of two vectors.

The proof for the resultant vector in Parallelogram addition is as follows,

Consider a parallelogram OABC as shown in the figure,

<a href="https://i.stack.imgur.com/gHNkO.jpg" rel="nofollow noreferrer"></a>

Let P&Q be two adjacent sides of parallelogram, and R be the resultant vector obtained by addition of vectors P&Q.

Now, drop a perpendicular from C on OA so that they meet at A

From right angled triangle ΔOCD,

OC²=OD²+DC²

[OD=OA+AD]

R²=(OA+AD)²+DC²

R²=OA²+AD²+2OA.AD+DC²

From ΔADC,

 AC²=AD²+DC²

and also cosθ=AD/AC

And hence R²=OA²+AD²+2OA.AD+DC²

And substituting A and B

R²=A²+B²+2A.Bcosθ

Now total time taken to hear the sound after dropping the stone = 4sec

It is time between throwing and listening

therefore time for sound to go from depth to the height = 2sec

speed of sound= 340m/s

therefore depth = time * speed

=2*340

=680m

Ans. The Zeroth Law of Thermodynamics states that if two bodies are each in thermal equilibrium with some third body, then they are also in equilibrium with each other.

The first law, also known as Law of Conservation of Energy states that energy cannot be created or destroyed in an isolated system.

Ans. The particular temperature and pressure at which the solid, liquid, and gaseous phases of a given substance are all at equilibrium with one another is known as Triple Point Water.

Ans. The amount by which unit length of a material increases when the temperature is raised by one degree is called the coefficient of linear expansion and is represented by \(\alpha\) (Greek alpha).

The amount by which unit area of a material increases when the temperature is raised by one degree is called the coefficient of superficial (i.e. area) expansion and represented by \(\beta\)(Greek beta).

Relation b/w both : 

\(\beta = 2 \alpha\)

Ans. Let Radius of big Drop is R and Radius of Small Droplet is r.

Then 

Volume of Big Drop = Volume of 1000 Small Droplets 

=> \({4\over 3} \times {{\pi} } \times R^3 = {1000}{ \times }{4 \over 3 }{\times \pi \times r^3}\)

=> \(r = {1\over 10} \times R \)

The Surface Energy of 1000 Droplets = \(1000 [{T \times 4\pi r^2}] \)

=> \(1000 [{T \times 4 \pi ({R\over 10})^2}]\)

=> \(10 [T\times 4\pi R^2]\)     ......... (1)

The Surface Energy of Big Drop = \(T \times 4\pi R^2\)

Ratio of Surface energy :

\(10 [T\times 4\pi R^2] : [T\times 4\pi R^2] = 10:1 \)

Surface Energy Decrease in This Case. 

Ans.  Steady State is a State or Condition of a system or process (as one of the energy states of an atom) that does not change in time.

In other Words, A condition that changes only negligibly over a specified time.

25C

Ans. 

• Static friction acts because the body tends to move when a force is applied on it.
• Limiting friction is the friction on a body just before it starts moving. Generally,limiting friction is highest. 
• Kinetic friction is the friction which acts on the body when the body is moving.

An artificial satellite constitutes a freely falling body.Hence,the effective gravity inside a satellite is zero.

If g=0,its time period becomes infinite .that's why pendulum will not oscillate .In other words, it will oscillate with a time period.

Yes, it will escape because its velocity will become equal to the escape velocity.