Paper 2 physics questions with solutions

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• NumericdifficultUnit dimension and errorunit and conversion of units

  In a new system of units, the units of mass, length, time and current are 5 kg, 5 m, 5 s and 5 A, respectively. If μ₀ and ε₀ are the permeability and permittivity of free space, respectively, then in this new system of units, the magnitude of one SI unit of √(μ₀/ε₀), is:

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• ParagraphdifficultCapacitorcapacitor with dielectric

  A container of height 2 m, length 2 m and breadth 1 m is made of insulating vertical walls and two large area horizontal metal plates M₁ and M₂ which extend far beyond the vertical walls in all directions. The container is partitioned into two equal chambers with a thin insulating vertical wall. The partition wall contains a small hole of cross-sectional area √10 cm² near its bottom edge. Initially the hole is closed and the left chamber of the container is completely filled with a liquid of dielectric constant ε(r) = 15 and the right chamber is empty, ε(r) = 1. At time t = 0, the hole is opened and the liquid flows from the left chamber to the right chamber. In both the chambers, the space above the liquid has ε(r) = 1 and is maintained at atmospheric pressure. The schematic of the container at a time t > 0 is shown in the figure. [Given: acceleration due to gravity is 10 m s⁻².]

  

  Sub-question 1

  The height (in m) of the liquid in left chamber at t = 500 s is:

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  Sub-question 2

  The difference in the capacitance (in F) between the metal plates at t = 0 and that at t = 500 s is (8 - n)ε₀, where ε₀ is the permittivity of free space. The value of n is:

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• Multi-correctmediumThermodyanmicsthermodynmic process and work done

  Ten moles of an ideal monoatomic gas, initially in state a at atmospheric pressure and temperature T(a) = 27°C, is enclosed in a metal cylinder of volume V₀ fitted with a frictionless piston. The gas is suddenly compressed to state b with volume V₀/3. Now, keeping the piston stationary, the cylinder is submerged in a water bath of temperature 11°C until the gas reaches the temperature of the water bath, which is denoted as state c. Finally, while still in the water bath, the piston is brought slowly to its initial position, which is denoted as state f. If R is universal gas constant, then the correct option(s) is/are: [Given: 9^(1/3) = 2.08]

  Select all that apply

  • Option A

    The schematic P-V diagram of the processes described above is as shown in figure.

    
  • Option B

    The change in internal energy in going from state a to b is 4860R.

  • Option C

    The net change in the internal energy in the whole process is -240R.

  • Option D

    The pressure and temperature of the state b are 2.08 times the atmospheric pressure and 624 K, respectively.

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• MCQmediumNuclear physicsradioactivity and law of decay

  A nuclear reactor starts producing a radioactive nuclide X from t = 0, at a constant rate of α per second. Each decay of X produces energy E₀, which is utilized to heat a liquid of mass m and specific heat s. Assuming no heat loss from the liquid and taking λ as the decay constant of X, the rate of increase in the temperature of the liquid is:

  Options

  • Option A

    αE₀(ms)⁻¹(1 - e⁻λᵗ)

  • Option B

    αE₀(ms)⁻¹(eλᵗ - 1)

  • Option C

    λE₀(ms)⁻¹(1 - e⁻λᵗ)

  • Option D

    E₀(ms)⁻¹(α - λe⁻λᵗ)

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• MCQmediumGeometrical opticsprism and thin prism

  A beam of polychromatic light passes through a thin prism of prism angle 6°. The refractive index of the material of the prism varies with wavelength λ as n(λ) = αλ + β/λ², where α = 3 μm⁻¹ and β = 0.096 μm². If λ(min) is the wavelength at which the angle of minimum deviation D(min) is smallest, then the correct value of D(min) at λ(min) is:

  Options

  • Option A

    6.4°

  • Option B

    4.8°

  • Option C

    3.2°

  • Option D

    2.4°

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• NumericdifficultWave Opticsdiffraction of light

  In a single slit diffraction experiment, a slit of width (0.016 ± 0.002) mm is used to measure the wavelength of a monochromatic light source. In the diffraction pattern, the angular distance between the central maximum and first minimum is measured to be (2° ± 40′). The value of the fractional error in the measurement of wavelength is: [Given: sin(2°) = 0.035]

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• ParagraphdifficultRotational Motionangular impulse in pure rotation and rotational collision

  A uniform circular disk of radius 0.2 m and mass 1 kg is pivoted at its top point C such that it can rotate freely around C in the XY plane, as shown in the figure. Initially, when the disk is at rest, a particle of mass 20 g, travelling along negative x direction in the XY plane with speed 100 m s⁻¹, hits the circumference of the disk at a point P. After collision the particle moves along negative y direction at a speed of 90 m s⁻¹. [Given: acceleration due to gravity g = -10ĵ m s⁻².]

  

  Sub-question 1

  After the collision the disk starts to rotate around point C in the XY plane. The maximum change in the height (in m) of its center O is:

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  Sub-question 2

  Amount of energy loss (in J) in the collision is:

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• NumericmediumWave Opticspolarisation

  As shown in the figure, a ray AB of unpolarized light enters from water of refractive index n(w) = 4/3 into a medium of refractive index n(p) = 4/√3 after passing through a glass plate of refractive index n(g) = 1.5 and a layer of water. At a particular incident angle i the reflected ray CD is polarized in the direction as shown in the figure. The value of i (in degrees) is:

  

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• NumericdifficultCurrent electricityelectric instruments

  As shown in the figure, the resistance of a galvanometer G can be found by the half-deflection method. Here the resistance R₂ is adjusted such that when the key K is closed the deflection in the galvanometer becomes half of the value as compared to when K is open. Half-deflection is obtained at R₂ = 4 Ω and thus the galvanometer resistance is found to be 6 Ω. In this half-deflection condition the current (in mA) through the resistor R₁ is:

  

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• NumericmediumUnit dimension and errorvernier callipers and screw gauge

  Two thin wires, Wire-1 of diameter 0.650 mm and Wire-2 of unknown diameter d are given. To obtain the value of d, the diameters of the two wires are measured with a screw gauge. The screw gauge has a pitch of 0.5 mm and there are 100 divisions on the circular scale (CS). The smallest division on the linear scale (LS) is 0.5 mm. The table shows the readings of LS and CS for the measurements. The value of d (in μm) is:

  

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