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IAF Group X 2020 Physics Test - 14
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IAF Group X 2020 Physics Test - 14
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  • Question 1/10
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    The temperature when the surface tension of water would be minimum:

    Solutions

    Concept-

    Surface tension (S) - It is the property by virtue of which the free surface of a liquid at rest behaves like an elastic stretched membrane tending to contract so as to occupy minimum surface area.

    Surface tension is measured as the force acting per unit length of an imaginary line drawn on the liquid surface.

    Surface tension = Force/Length

    There are two factors which can affect the surface tension of a liquid and they are:

    • Temperature: If temperature increases then the surface tension of a liquid decreases.
    • Soluble Impurities: In the case of less soluble impurities, the surface tension decreases. But, for highly soluble impurities in the liquid the surface tension increases.​

    Explanation-

    Effect of temperature on surface tension - When a liquid is heated, the kinetic energy of its molecules increases and the intermolecular attraction becomes weaker.

    Hence, surface tension decreases when the temperature increases because cohesive forces decrease with an increase in molecular thermal activity. 

    Hence among the given options surface tension of water will be minimum at 75° C.

     

  • Question 2/10
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    Find the uniform angular acceleration of a wheel if its angular speed increases from 420 rpm to 660 rpm in 8 seconds?

    Solutions

    Concept-

    Angular acceleration (α)

    The rate of change of angular velocity of a particle is called its angular acceleration. If Δ ω is the change in angular velocity in time Δ t, then then average angular acceleration is:

    α = Δω/Δt

    Relations between ω, ν and T

    By definition of time period, a particle completes one revolution in time T i.e. it travels an angle of 2π in time T.

    ∴ t = T

    Angular displacement (θ) = 2π radian

    Angular velocity = Angular displacement / time

    ω = θ/t = 2π/T

    ω = 2π ν     ∴1/T = ν

    Explanation-

    Given:– t = 8 sec,

     

  • Question 3/10
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    The product of the moment of inertia and the angular acceleration is:

    Solutions
    • Torque is the measure of the amount of force acting on an object that can cause it to rotate.
    • The torque that is needed to produce angular acceleration depends on the mass distribution of the object which is described by the moment of inertia. Therefore, torque (τ) is the product of the angular acceleration (a) and the moment of inertia (I) of an object.

          τ = I × a

    • Angular acceleration is the rate of change of angular velocity and moment of inertia is a measure of how easily a body can be rotated.

     

  • Question 4/10
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    The kinetic energy of molecular motion appears as

    Solutions

    According to kinetic energy theory, if we increase the temperature of a gas, it will increase the average kinetic energy of the molecule, which will increase the motion of the molecules. This increased motion increases the outward pressure of the gas.

    The average kinetic energy of the gas molecule only depends upon temperature. Increasing the temperature increases the translational motion of molecules Energy is related to temperature by the relationship:

    E = kT where E = kinetic energy, k = constant and T = temperature

     

  • Question 5/10
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    The fraction of a ball floating inside the liquid depends upon

    Solutions

    Concept-

    Archimedes Principal

    It states that when a body is partially or wholly immersed in a fluid, it experiences an upward thrust equal to the weight of the fluid displaced by it and its upthrust acts through the center of the gravity of the displaced fluid.

    Apparent weight of immersed body

    The actual weight W of the immersed body acts downward and the upthrust U acts upwards.

    ∴ Apparent weight = Actual weight – Buoyant force

    Wapp = W – U

    Wapp = Vσ g – Vρ g = Vg(σ  - ρ)

    Where, V = volume of the liquid, σ = density of the body, ρ = density of the liquid and g = acceleration due to gravity.

    Solution-

    Consider a body of height h and density σ, lying inside a liquid of density ρ, at a depth x below the free surface of the liquid. Then the apparent weight of the immersed body is

    Wapp = Vσg – Vρg = Vg(σ  - ρ)

    ∴ The fraction of a ball floating inside the liquid depends upon both, the density of the liquid and density of the ball.

     

  • Question 6/10
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    Statement 1: Damping coefficient c for over damped oscillation is lesser than 2mωn

    Statement 2: Damping coefficient c for under damped oscillation is greater than 2mωn

    Solutions

     

  • Question 7/10
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    A magnet is freely suspended in a constant magnetic field. Calculate the work done if the magnet is deflected by an angle α from the initial direction. M = magnetic moment, H = Magnetic Field

    Solutions

    Concept-

    Potential energy of a magnetic dipole in a magnetic field Potential energy of a magnetic dipole in a magnetic field is the energy possessed by the dipole due to its particular position in the field.

    When a magnetic dipole of moment  is held at an angle θ with the direction of a uniform magnetic field , the magnitude of the torque acting on the dipole is

    τ = MBsinθ       ----(i)

    This torque tends to align the dipole in the direction of the field. Work has to be done in rotating the dipole against the action of the torque. This work done is stored in the magnetic dipole as potential energy of the dipole. Now, small amount of work done in rotating the dipole through a small angle dθ against the restoring torque is

    dW = τ dθ = MBsinθ dθ

    Total work done in rotating the dipole from θ1 to θ2 is

    ∴ Potential energy of the dipole is

    U = W = -MB (cosθ– cosθ1)

    Explanation-

    Given- Magnetic dipole of moment M, uniform magnetic field is H and angle α is the direction.

    α= 0 and  α1 = α

    ∴ the total work done in rotating the dipole from α1 to α2 is

    W = -MH (cosα– cosα1)

    W = -MH (cosα  – cos0)

    W = -MH (cosα  – 1)

    W = MH (1 - cosα)

     

  • Question 8/10
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    Given below are facts about the Rutherford model of atomic structure. Identify the incorrect one.

    A. The positive charge and most of the mass of the atom was densely concentrated in extremely small region.

    B. Rutherford gave the ‘plum-pudding’ model.

    C. Protons and neutrons are held together by electrostatic forces of attraction.

    Solutions

    Concept-

    JJ Thomson Thomson’s model:

    • He proposed that an atom is a sphere of positively charged matter with electron embedded in it. The positive charge is uniformly distributed over the entire atom.
    • The arrangement of electrons inside the continuous positive charge is similar to that of the seeds in a watermelon or plums in pudding. That is why Thomson’s model is also known as ‘plum-pudding’ model.

    Rutherford model of atomic structure:

    • As most of the α – particle pass straight through the foil, so most of the space within the atom must be empty.
    •  Rutherford suggested that all the positive charge and the mass of the atom is concentrated in a very small region, called the nucleus of the atom.
    • The nucleus is surrounded by the cloud of electrons whose total negative charge is equal to the total positive charge on the nucleus, so that the atom as a whole is electrically neutral.

    Explanation-

    • JJ Thomson gave the ‘plum-pudding’ model. ‘Plum-pudding’ model came before the discovery of the nucleus. Rutherford gave ‘nuclear model’ of atom (similar to the solar system).
    • Electrons and nucleus are held together by electrostatic forces of attraction. Protons and neutrons have “nuclear force” between them.
    • The positive charge and most of the mass of the atom was densely concentrated in extremely small region. (small portion region – nucleus).

     

  • Question 9/10
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    What is the dimensional formula of the universal gravitational constant?

    Solutions

    CONCEPT:

    • Newton's law of Gravitation: It states that everybody in this universe attracts every other body with a force, which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
      • The direction of the force is along the line joining the particles.

    The magnitude of the gravitational force F is given by:

    Where G = universal gravitational constant, M1 = mass of 1st body, M2 = mass of 2nd body and R = distance between the two bodies.

    EXPLANATION:

    • The dimensional formula is defined as the expression of the physical quantity in terms of mass, length, time and ampere.

    The above equation can be written as,

    Now,

    Force = mass × acceleration

    ∴ Dimensional formula of force (F) = [M] × [LT-2] = [MLT-2]

    Dimensional formula of radius (R2) = [L2]

    Dimensional formula of radius (M) = [M]

    Dimensional formula of universal gravitational constant (G)

    ∴ The dimensional formula of universal gravitational constant G is [M-1L3T-2].

     

  • Question 10/10
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    To obtain n-type semiconductor the impurity added to pure semiconductor is

    Solutions

    Intrinsic semiconductor + Pentavalent = n – type semiconductor

    Intrinsic semiconductor + Trivalent = p – type semiconductor

     

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