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Physics Test - 1
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  • Question 1
    1 / -0.25

    The Atom bomb and the hydrogen bomb are based on the principles of:

    Solution

    CONCEPT:

    • Nuclear fission is a nuclear reaction process in which a heavy nucleus splits into two nuclei of nearly equal mass.
      • Nuclear fission of heavy elements was discovered by German Otto Hahn with the help of Fritz Strassman.
      • Nuclear fission is the opposite of the nuclear fusion reaction.
      • Splitting apart uranium, into smaller atoms such as iodine, strontium, xenon, and barium is the example of a nuclear fission reaction

    • Nuclear fusion is the nuclear reaction in which two or more atomic nuclei are combined to form one or more different atomic nuclei and subatomic particles.
      • Sun and other stars generate light and heat by nuclear fusion.
      • A hydrogen bomb is an immensely powerful bomb whose destructive power comes from the rapid release of energy during the nuclear fusion of isotopes of hydrogen (deuterium and tritium), using an atom bomb as a trigger.

    EXPLANATION:

    • The principle behind the hydrogen bomb is based on uncontrollable nuclear fusion.
    • nuclear bomb based on the fission of uranium is placed at the core of the hydrogen bomb.
    • So hydrogen bomb is based on the principle of Nuclear Fusion Reaction.

     

  • Question 2
    1 / -0.25

    The minimum value of effective capacitance that can be obtained by combining 3 capacitors of capacitances 1 pF, 2 pF and 4 pF is

    Solution

    CONCEPT:

    • The device that stores electrical energy in an electric field is called a capacitor.
    • The capacity of a capacitor to store electric charge is called capacitance.
    • When two or more capacitors are connected end to end and have the same electric charge on each is called a series combination of the capacitor.

    Equivalent capacitance (Ceq) in series combination:

    • When two or more capacitors are connected in such a way that their ends are connected at the same two points and have an equal potential difference for all capacitor is called a parallel combination of the capacitor.

    Equivalent capacitance (Ceq) for parallel combination:

    Ceq = C1 + C2 + C3

    Where C1 is capacitance of first capacitor, C2 is capacitance of second capacitor and C3 is capacitance of third capacitor

    EXPLANATION:

    Given that:

    C= 1 pF

    C2 = 2 pF

    C3 = 4 pF

    The equivalent capacitance will be minimum when they all are connected in series combination.

    For series combination:

    Thus minimum effective capacitance will be equal to 4/7 pF when all three will be connected in series combination. Hence option 1 is correct.

    IMPORTANT POINTS:

    • When all the capacitors will be connected in parallel combination then the effective capacitance will be maximum.

     

  • Question 3
    1 / -0.25

    When a simple pendulum is taken to the pole from the equator then its time period will:

    Solution

    CONCEPT:

    Simple pendulum:

    • When a point mass is attached to an inextensible string and suspended from fixed support then it is called a simple pendulum.
    • The time period of a simple pendulum is defined as the time taken by the pendulum to finish one complete oscillation.

    • The above formula is only valid for small angular displacements.

    Where, T = Time period of oscillation, L = length of the pendulum, and g = gravitational acceleration

    Where, T = Time period of oscillation, L = length of the pendulum, and g = gravitational acceleration

    • By equation 1 it is clear that the time period of a simple pendulum is inversely proportional to the square root of the gravitational acceleration.
    • We know that the gravitational acceleration at the pole is more than the gravitational acceleration at the equator on the earth.
    • So we can say that the time period of a simple pendulum will be more at the equator compared to the pole.
    • So we can say that when a simple pendulum is taken to the pole from the equator then its time period will decrease. Hence, option 2 is correct.

    Additional Information

    • The amplitude of a simple pendulum is defined as the maximum distance traveled by the pendulum from the equilibrium position to one side.
    • The length of a simple pendulum is defined as the distance between the point of suspension to the center of the bob.
    • Since the motion of the bob is along a circle of length L and centre at the support point, the radial acceleration is given as,

    ⇒ aR = ω2L

    • The radial acceleration is provided by the net radial force T' - mg.cos θ.
    • The tangential acceleration is provided by mg.sinθ.
    • Torque τ about the support is entirely provided by the tangential component of a force and it is given as,

    ⇒ τ = -L.(mg.sin θ)

    • The negative sign shows that this is the restoring torque that tends to reduce angular displacement.
    • The tangential acceleration is given as,

     

  • Question 4
    1 / -0.25

    A person is unable to read a newspaper without his glasses. He is most probably suffering from

    Solution

    CONCEPT:

    • Visual defect: When the vision of any human being defected due to some defect in the eye is called a visual defect.

    There are three main types of defects.

    • Myopia or near-sightedness: In this defect of vision, the man can see the nearby object but can’t see the distant object clearly. It occurs when the eyeball is too long.
      • A concave lens is used to cure myopia.
    • Hypermetropia or farsightedness: In this defect of vision, the man can see the distant object but can’t see the nearby object clearly.
      • A convex lens is used to cure it.
    • Presbyopia: When the eye lens becomes less elastic then it happens.
      • When the Objects which nearby appear to be blurred to a person then it is called Presbyopia.

    EXPLANATION:

    • If a person is unable to read a newspaper without his glasses, which means a person can’t see a nearby object
    • Hence, we can say that he is suffering from far-sightedness and medically termed hypermetropia can be treated using a pair of concave lenses which is used in his glasses. So option 4 is correct.

    EXTRA POINTS:

    Defects of Vision

    Details

    Corrections

    Myopia or Near-sightedness

    The eye can see nearby objects clearly but the distant objects appear indistinct.

    Concave Lens

    Hypermetropia or Farsightedness

    The human eye can see Distant objects clearly but cannot see nearby objects distinctly.

    Convex Lens

    Astigmatism

    It’s a type of distorted or blurred vision at any distance.

    As per need

    Presbyopia

    People suffer from near-sightedness as well as farsightedness.

    bifocal lenses

     

  • Question 5
    1 / -0.25

    The force required to raise a circular ring of radius 4cm placed on the surface of water is : (Surface tension of water 75 dyne/cm)

    Solution

    The correct answer is option 4) i.e. 600π dyne.

    CONCEPT:

    • Surface tension is the tendency of water molecules to adhere to each other so as to form the minimum surface area possible.
      • This is a result of cohesion between water molecules.
      • Towards the interface of water with air, there will be no cohesive forces. Hence the net force acts downwards.
      • The top surface of the water will now act like a stretched membrane.

     

  • Question 6
    1 / -0.25

    If the empirical formula for the observed wavelengths for hydrogen is 1/λ = R(1/12 - 1/n2), where n is integral values higher than 1, then it represents the _____________ spectral series.

    Solution

    CONCEPT:

    • When excited electrons fall from higher energy level to lower energy level, they emit electromagnetic radiations of discrete frequencies and the emission spectrum is formed.
    • The spectral lines of the Lyman series fall in the U.V region for the Hydrogen atom.
    • We can predict this using this equation

    • Lyman series – when an electron from higher energy level falls to 1st energy level – UV region.
    • Balmer series – when an electron from higher energy level falls to 2nd energy level – Visible region.
    • Paschen series – when an electron from higher energy level falls to the 3rd energy level – Infrared region.
    • Brackett series – when an electron from higher energy level falls to 4th energy level – Infrared region.
    • Pfund series – when an electron from higher energy level falls to the 5th energy level – Infrared region.

    EXPLANATION:

    • In a hydrogen atom, the transition of electrons between different energy levels gives spectral lines of different wavelengths. These lines fall into a specific series.
    • We can predict this using this equation

    In the Lyman series, the spectral lines correspond to the transition of an electron from a higher to lower energy level when the quantum number of the final stationary orbit  ( nf ) is 1.

     

  • Question 7
    1 / -0.25

    In a typical stress-strain curve given below, the stress at point B is called ______________.

    Solution

    CONCEPT:

    • Stress-Strain Curve determines how a material behaves how it has a relationship between the strain and stress for a given material.
      • We apply a force on a material cylinder and record the change in length at various applied forces to cause the strain.

    The curve for steel looks as follows:

    • With the assistance of this curve, we can understand how the material behaves with increasing loads.
    • Analysis of the Curve
    1. The region between O and A, the curve is a straight line in this region. Hence, Hooke’s Law obeys in this region.
    2. Region from A to B, the stress is not proportional to strain in this region. However, if we remove the load the body will return to its original dimension.
    3. Point B for a typical stress-strain curve is the elastic limit or Yield Point and the stress at this point is the Yield Strength (Sy) of the material. This is the point upto which, when the load is removed, the body still returns to its original dimension.​

    EXPLANATION:

    • Point B is the point up to which a material behaves as an elastic body.
    • This point is known as the elastic limit point or yield point.
    • And the stress at this point is known as yield strength.
    • So the point up to which a material behaves as an elastic body is yield strength (strength at point B).
    • Hence the correct answer is option 1.

     

  • Question 8
    1 / -0.25

    Electrons used in an electron microscope are accelerated by a voltage of 25 kV. If the voltage is increased to 100 kV then the de-Broglie wavelength associated with the electrons would

    Solution

    Concept:

    • The wavelength of the electron due to its motion is called the de-Broglie wavelength of the electron.
    • The bundle of light rays is called a photon.
    • The de-Broglie wavelength of an electron (λe) is given by:

    Where h = Plancks constant, m = mass of the particle, V = Velocity

    • The de Broglie wave equation explains the dual nature of matter as it connects the wave characteristics, λ to particle characteristics P.
    • The wavelength of an electron accelerated through a potential V is given by

    Calculation:

    Given - Voltage (V1) = 25 kV, Voltage (V2) = 100 kV

    De Broglie wavelength in terms of accelerated potential is given by

    When the voltage was increased from 25Kv to 100 Kv then the de-Broglie wavelength associated with the electrons would decrease by 2 times. Therefore option 3 is correct.

     

  • Question 9
    1 / -0.25

    The work done in carrying a charge q once around a circle of radius r with a charge Q placed at the center will be

    Solution

    CONCEPT:

    Electric potential (V):

    • The potential difference between two points in an electric field may be defined as the amount of work done in moving a unit positive charge from one point to the other against the electrostatic force i.e.,

    • The electric potential V at a point P due to point charge +q at a distance r is given by

    EXPLANATION:

    • As charge +Q is placed at the center of the circle, therefore the electric potential will be the same on its circumference as the distance is the same. Thus it is an equipotential surface.
    • As we know that the potential at each point on an equipotential surface is the same.

    ∴ Potential difference is

    ΔV = V2 - V1 = V - V = 0

    • Therefore the amount of work done in moving a charge q from one point to another around a circle of radius r is

    ⇒ Work done = q ΔV = q × 0 = 0

     

  • Question 10
    1 / -0.25

    The energy stored in a parallel plate capacitor is E and the potential difference between the plates is V, then the E is related to V as:

    Solution

    CONCEPT:

    Capacitor:

    • The capacitor is a device in which electrical energy can be stored.
      • In a capacitor two conducting plates are connected parallel to each other and carrying charges of equal magnitudes and opposite sign and separated by an insulating medium.
      • The space between the two plates can either be a vacuum or an electric insulator such as glass, paper, air, or semi-conductor called a dielectric.​

    ​Parallel plate capacitor:

    • A parallel plate capacitor consists of two large plane parallel conducting plates separated by a small distance.
      • The space between the two plates can either be a vacuum or an electric insulator such as glass, paper, air, or semi-conductor called a dielectric.​

    The energy stored in the capacitor is given as,

    Energy density:

    • It is defined as the energy stored per unit volume of space between the plates.
    • Energy density u between the plates is given as,

    Where C = capacitance of the capacitor, Q = charge on the plates, V = potential difference between the plates, and E = electric field intensity between the plates

    EXPLANATION:

    Given U = E

    We know that the energy stored in the capacitor is given as,

    Additional Information

    Parallel plate capacitor:

    • A parallel plate capacitor consists of two large plane parallel conducting plates separated by a small distance.
      • The space between the two plates can either be a vacuum or an electric insulator such as glass, paper, air, or semi-conductor called a dielectric.​
      • The electric field intensity at the outer region of the parallel plate capacitor is always zero whatever be the charge on the plate.
      • The electric field intensity in the inner region between the plates of a parallel plate capacitor remains the same at every point.
      • When the dielectric medium is filled in the space between the plates of the parallel plate capacitor, its capacitance increases.
    • The electric field intensity in the inner region between the plates of a parallel plate capacitor is given as,

    ​Where A = area of the plates, d = distance between the plates, Q = charge on the plates, σ = surface charge density, E = electric field between the plates, and K = dielectric constant

     

  • Question 11
    1 / -0.25

    What is the force between two small charged spheres having charges of 2 × 10-7 C and 3 × 10-7 C placed 30 cm apart in the air?

    Solution

    CONCEPT:

    Coulomb's law in Electrostatics –

    • Coulomb's law state’s that force of interaction between two stationary point charges is directly proportional to the product of the charges, and inversely proportional to the square of the distance between them and acts along the straight line joining the two charges.

     

  • Question 12
    1 / -0.25

    If the temperature of a conductor increases, then its resistance also increases because

    Solution

    CONCEPT:

    • Resistance (R): The resistance offered to the flow of current is known as the resistance.
    • SI unit of resistance is the ohm (Ω).
    • Mathematically resistance can be written as

    Where m = mass of electron, e = charge of electron, n = No. of free electrons per unit volume in conductor,  l = length, ρ = resistivity, A = Area of cross-section of conductor and τ = relaxation time

    EXPLANATION:

    • From above it is clear that resistance of a wire depends on the number of free electrons per unit volume in conductor, lengtharea of cross-sectionrelaxation time.
    • From above it is clear that resistance of the wire is inversely proportional to relaxation time and relaxation time is inversely proportional to temperature. Therefore if the temperature of a conductor increases, then relaxation time decreases. Therefore option 1 is correct.
    • As we know that there will be no effect on the mass of the electrons if temperature increases. Therefore option 2 is incorrect.
    • Therefore if the temperature of the wire increases, then the electron density increases as the number of free electrons per unit volume in the conductor will increase. Hence option 3 is incorrect.

     

  • Question 13
    1 / -0.25

    Find the effective resistance between points A and B.

    Solution

    CONCEPT:

    • Resistance: The measure of the opposition to current flow in an electrical circuit is called its resistance. 

    Resistance is calculated by:

    where l is its length, A area, and ρ is its metal resistivity. 

    • In the Series circuit, the equivalent resistance is the algebraic sum of all the resistances.

    Req = R1 + R2 + R3 +......  (In Series)

    • And in the Parallel circuit, the reciprocal of the equivalent resistance is the algebraic sum of all the reciprocal of the resistances.

    1/Req = 1/R1 + 1/R2 + 1/R3 +...... (in Parallel)

    EXPLANATION:

    On combining a series combination of R & R, the equivalent resistance is R1

    On combining a parallel combination of R1 & R, the equivalent resistance is RAB

     

  • Question 14
    1 / -0.25

    If an object is placed at a distance of f from the convex mirror of focal length f, then distance of image from the mirror will be:

    Solution

    The correct answer is option 4) i.e. f/2.

    CONCEPT:

    • Mirror formula for spherical mirrors: It is a formula that gives the relationship between the focal length "f" of the mirror, image distance from the mirror "v", and objects distance from the mirror "u".

    The mirror formula is given as:

    • Sign Convention for plane mirror: All the distances measured towards the left of the mirror are taken as negative and that towards the right of the mirror is taken as positive.
      • All the distances measured above the principal axis are taken positive and those measured below the principal axis are taken as negative.

    CALCULATION:

    Given that,

    The focal length of the mirror, f = f

    The object distance from the mirror, u = -f

    To find the image distance from the mirror, v

    Using mirror formula

     

  • Question 15
    1 / -0.25

    The electrons in the beam of a television tube move horizontally from South to North. The vertical component of the earth's magnetic field points down. The electron is deflected towards _____

    Solution

    CONCEPT:

    • Fleming Left-hand rule gives the force experienced by a charged particle moving in a magnetic field or a current-carrying wire placed in a magnetic field.
    • It states that "stretch the thumb, the forefinger, and the central finger of the left hand so that they are mutually perpendicular to each other.
    • If the forefinger points in the direction of the magnetic field, the central finger points in the direction of motion of charge, then the thumb points in the direction of force experienced by positively charged particles."

    • The magnitude of the force is given by 

    ⇒ F = I(L × B)

    Where I = Amount of current flowing through the conductor, B =  Magnetic field, and L = Length of conductor

    EXPLANATION:

    • Given that electrons in the beam of a television tube move horizontally from South to North that means current (I) is flowing from North to South.
    • The vertical component of the earth's magnetic field points down, which means it is acting in the eastern direction.
    • Hence the electrons are deflected toward the West. Therefore option 1 is correct.

     

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