Physics Test 230

The correct answer is option 4) i.e. L = √(2EI)

CONCEPT:

• Angular momentum: The angular momentum of a rigid object is defined as the product of the moment of inertia and the angular velocity.
  • Angular momentum also obeys the law of conservation of momentum i.e. angular momentum before and after is conserved.

Angular momentum, L = I × ω 

Rotational kinetic energy: For a given fixed axis of rotation, the rotational kinetic energy is given by:

CONCEPT:

Degrees of freedom (f) : It is the minimum number of coordinates required to describe the complete configuration of the system.

Degrees of freedom of a monoatomic molecule = 3

Degrees of freedom of a diatomic molecule = 5

Relation between d.o.f (f) and Cv

Concept-

• The atoms have protons and neutrons in the nucleous of the atom and electrons revolve around the nucleous in the orbits.
• For each orbits there is a certain amount of energy for the electrons.

The energy of electrons in any orbit is given by:

CONCEPT:

• Equilibrium: It is a state of a body in which overall change in a body is zero.
• Translational Equilibrium: A body is said to be in translational equilibrium if the net sum of all the forces (F) acting on a body is zero.

Σ F = 0

F_net = 0

F₁ + F₂ + F₃+ ............... + F_n = 0

• Rotational Equilibrium: A body is said to be in rotational equilibrium if the net sum of all the torque (τ) acting on a body is zero.

Σ τ = 0

τ_net = 0 

τ₁ +τ₂ + τ₃ + .................. + τ_n = 0

EXPLANATION:

• A body is said to be in equilibrium if it is in translational equilibrium and rotational equilibrium.
• Both translational and rotational equilibrium is required to a body in equilibrium.

Hence option 4 is correct.

Additional Information

• Solving the numerical problem on the equilibrium of forces always draws the FBD (Free Body Diagram). 
• A simplified version of the body on which all external forces are shown is called FBD (Free Body Diagram) of the given body.

CONCEPT:

• Cathode rays: Cathode rays are the stream of high speed negatively charged particles moving from cathode to anode in a discharge tube.
• The specific charge is defined as the ratio of charge to mass ratio of the electron.

Properties of Cathode Rays:

• Cathode rays travel in a straight line.
• They are streams off fast-moving electrons.
• Cathode rays heat up the material on which they fall.
• The cathode rays in the discharge tube are the electrons produced due to the ionization of gas and that emitted by cathode due to the collision of positive ions.
• Cathode rays are emitted normally from the cathode surface. Their direction is independent of the position of the anode. 
• Cathode rays are deflected by an electric field and also by a magnetic field.
• Cathode rays ionize the gases through which they are passed.
• Cathode rays can penetrate through thin foils of metal.

EXPLANATION:

• As an electron beam accelerated from cathode to anode its loss in potential energy appears as gain in the K.E. at the anode.
• If suppose V is the potential difference between cathode and anode then, loss in potential energy = eV,

• If both the fields are applied simultaneously and adjusted such that the electron beam passes undeflected and produces illumination at point P.

CONCEPT:

Electric potential is equal to the amount of work done per unit charge by an external force to move the charge q from infinity to a specific point in an electric field.

Shortcut Trick

Equal and opposite charges are placed on A(a,0) and B(-a,0). Also point P(0,c,d) is equidistant from A and B. Therefore the potential on P due to charges placed on A and B will be equal in magnitude but opposite in sign. Thus the total potential due to the two charges on D will be zero.

CONCEPT:

Leakage current: When a capacitor is connected with a voltage V, two plates of the capacitor get charged by charges +q and -q. 

No, current passes through the capacitor. Now, when a dielectric is added inside the capacitor, the charges get a medium through which

they can cross the distance between the plates and give some current as a result inside the capacitor. This current is known as the leakage current of the capacitor. 

Resistivity: It is equal to the resistance of a material per unit length and per unit area. 

Mathematically, Reisistance R = ρl/A

Resistivity ρ = RA/l 

Capacitance: C = kϵ₀A/d  

where, k = dielectric constant = relative permittivity, ϵ₀ = permittivity of the free space ,

d = distance between the plates, A = Area of the plates    

EXPLANATION:

When the material is filled between the plates of the parallel capacitor 

The capacitance C = kϵ₀A/d

∴ d/A = kϵ₀/C

Then the resistance of the material = R = ρd/A = ρkϵ₀/C

∴ The leakage current I = V/R = V/(ρkϵ₀/C) = VC/ρkϵ₀

CALCULATION

Given, 

V = 40 V, C = 2 pF = 2 × 10^-12 F

ρ = 200 Ωm, k = 50           

∴ The leakage current I = VC/ρkϵ₀

⇒ I = (40×2 × 10^-12) / (200×50×8.85×10^-12) = 0.9 mA

Hence the correct answer is option 2.

Concept:

• A light-emitting diode (LED) is a semiconductor device that emits visible light when an electric current passes through it
• Light Emitting Diode (LED) works only in the forward bias condition

• When free electrons reach the junction or depletion region, some of the free electrons recombine with the holes in the positive ions
• Free electrons recombine with holes in the depletion region
• Similarly, holes from p-side recombine with electrons in the depletion region

Kirchhoff’s Voltage Law: The algebraic sum of voltage (or voltage drops) in any closed path of the network that is traversed in a single direction is zero.

Here, the assumed current I causes a + ve drop of voltage when flowing from +ve to – ve potential while – ve drop of voltage when a current flowing from – ve to + ve for the above circuit,

 If we apply KVL,

CONCEPT:

According to the Ampere's circuital law,

The magnetic field inside the current carrying cable is written as:

Hence,  option 2) is the correct choice.

CONCEPT:

The Quality factor: Quality factor of resonance is a dimensionless parameter that describes how underdamped an oscillator or resonator is.