Paper 1 physics questions with solutions

Showing 1–10 of 16 questions

• NumericmediumThermodynamicscyclic process its effeciency ,second law of thermodynamics

  As shown in the figure, five Carnot engines, each with efficiency η and same number of cycles per unit time, are operating between six heat reservoirs. The amount of heat released per cycle by one engine is completely absorbed by the next engine. Consider Q₀ to be the amount of heat absorbed per cycle by the first engine and W as the amount of total work done by all the engines per cycle, then the net efficiency of the system is found to be η(net) = W/Q₀ = 211/243. The value of η is:

  

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• Multi-correctmediumElectromagnetic wavedisplacement current and properties of electromagnetic wave

  The electric field associated with an electromagnetic wave travelling in vacuum is given by E₀ sin(3y + 4z + ωt) î, where ω is the angular frequency. All quantities are in SI units. The correct statement(s) about this wave is/are: [Given: speed of light in vacuum c = 3 × 10⁸ m s⁻¹.]

  Select all that apply

  • Option A

    The wave is travelling in -(1/5)(3ĵ + 4k̂) direction.

  • Option B

    The magnitude of the wave vector is 0.5 m⁻¹.

  • Option C

    The value of ω is 1.5 × 10⁹ rad s⁻¹.

  • Option D

    The magnetic field associated with this wave is given by (E₀/c) sin(3y + 4z + ωt)(4ĵ - 3k̂).

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• MatchmediumGeometrical opticsdespersion of light ,despersive power and combination of prism

  In List-I, four optical effects are mentioned. The physical phenomena of light which are essential to describe these optical effects are given in List-II. Choose the option which describes the correct match between the entries in List-I to those in List-II.

  List 1

  1. (P) Colorful sky in north polar region (Aurora Borealis)

  2. (Q) Partially polarized sun light

  3. (R) Rainbow

  4. (S) Dark and bright fringes

  5. .

  List 2

  1. (1) Dispersion and reflection

  2. (2) Total internal reflection

  3. (3) Diffraction

  4. (4) Scattering of light by molecules in the atmosphere

  5. (5) Emission of radiation from oxygen and nitrogen atoms excited by charged particles

  Options

  • Option A

    P→5, Q→4, R→1, S→3

  • Option B

    P→4, Q→2, R→1, S→3

  • Option C

    P→4, Q→1, R→2, S→3

  • Option D

    P→5, Q→4, R→1, S→2

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• MatchmediumWave Motionstationary wave in sound and organ pipe ,resonance tube

  List-I shows four configurations made of straight and semi-circular narrow tubes containing air. A sound wave of wavelength λ = 0.29 m enters these structures at the point S and a sound detector is placed at D. Between the points S and D, the sound travels only through the tubes. List-II contains the possible smallest values of l for which the detector D records maximum amplitude. Ignore effects of sharp corners. [Given cos15° = 0.97] Choose the option that best describes the match between the entries in List-I to those in List-II. Image

  List 1

  1. 

  2. 

  3. 

  4. 

  5. .

  List 2

  1. (1) 1.32 m

  2. (2) 1.19 m

  3. (3) 0.51 m

  4. (4) 0.29 m

  5. (5) 0.13 m

  Options

  • Option A

    P→4, Q→3, R→5, S→1

  • Option B

    P→4, Q→3, R→1, S→5

  • Option C

    P→3, Q→4, R→1, S→2

  • Option D

    P→3, Q→4, R→5, S→2

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• Multi-correctmediumThermodynamicsthermodynmic process and work done

  A quasi-static cycle of a monoatomic ideal gas contains an isothermal process (ab), followed by an isochoric process (bc) and an adiabatic process (ca) as shown in the figure. The volumes of the gas are V₁ and V₂ at a and b, respectively. If the cycle has heat input Q(in) and output Q(out), then the efficiency of the cycle is defined as η = [Q(in) - Q(out)]/Q(in). The correct statement(s) is/are: [Given: ln2 ≈ 0.7]

  

  Select all that apply

  • Option A

    If V₂/V₁ = 8, the heat released in the process bc is smaller than the heat absorbed in the process ab.

  • Option B

    For a given value of V₂/V₁, η does not depend on the temperature of the isothermal process.

  • Option C

    If V₂/V₁ = 8, then the temperature of the gas at a is 4 times the temperature of the gas at c.

  • Option D

    If V₂/V₁ = 8, then the pressure of the gas at a is 4 times the pressure of the gas at b.

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• MCQmediumRotational Motioncombined translatory and rotatory motion ,Pure rolling motion

  A solid cylinder of radius R rolls without slipping with a center of mass speed v₀ = √(gR/3) on a horizontal surface with a vertical edge, as shown in the figure. Here, g is the acceleration due to gravity. At the moment when the cylinder loses contact with the surface due to rotation around the corner, the speed of its center of mass is:

  

  Options

  • Option A

    0

  • Option B

    √(5gR/7)

  • Option C

    √(gR/15)

  • Option D

    √(3gR/7)

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• MCQmediumRotational Motioncombined translatory and rotatory motion ,Pure rolling motion

  Consider a large disk of radius R and two smaller disks, each of radius r = R/50, lying on its circumference, as shown in the figure. The smaller disks are initially in contact with each other, with an angular separation Δθ between their centers. They are made to roll without slipping in opposite directions, with constant angular velocities ω and 2ω while the large disk is held stationary. The time τ at which the smaller disks are again in contact is: [Use sin(Δθ) = Δθ and ignore gravity.]

  

  Options

  • Option A

    τ = 51(2π - 4/51)/ω

  • Option B

    τ = 51(2π - 2/51)/(3ω)

  • Option C

    τ = 51(2π - 4/51)/(3ω)

  • Option D

    τ = 51(2π - 2/51)/ω

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• MatchmediumRotational Motionmoment of inertia and kinetic energy in pure rotation

  List-I shows four planar structures made of uniform solid rods each of mass m and length l. In List-II the possible moments of inertia of these structures about an axis OCO′, which lies in the plane of the structures, are given. Choose the option that describes the correct match between the entries in List-I to those in List-II. Image

  List 1

  1. (P)

     

  2. I

     (Q)

     

  3. (R)

     

  4. (S)

     

  5. .

  List 2

  1. 1. 1. (5/4)ml²

  2. 1. 2. (1/6)ml²

  3. 3. 3. (1/12)ml²

  4. 1. 4. (2/3)ml²

  5. 1. 5. (1/3)ml²

  Options

  • Option A

    P→5, Q→1, R→4, S→2

  • Option B

    P→1, Q→3, R→4, S→2

  • Option C

    P→5, Q→3, R→2, S→1

  • Option D

    P→5, Q→4, R→2, S→1

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• Multi-correctmediumAtomic Structure and X-raysatomic structure and bohr atomic model

  Consider a hydrogen atom with vₖ, rₖ, and Kₖ denoting the velocity, orbital radius and kinetic energy of the electron in the kth orbit, respectively. The electron undergoes a transition from the nth orbit, emitting radiation corresponding to the Lyman series. Considering h to be Planck’s constant and ε₀ the permittivity of free space, the correct statement(s) is/are:

  Select all that apply

  • Option A

    Magnitude of change in kinetic energy of electron can be expressed as (h/4π)|nvₙ/rₙ - v₁/r₁|.

  • Option B

    Magnitude of change in de Broglie wavelength of the electron can be expressed as [e²/(4ε₀)]|1/Kₙ - 1/K₁|.

  • Option C

    Frequency of the radiation emitted can be expressed as [e²/(8πε₀h)](1/r₁ - 1/rₙ).

  • Option D

    Magnitude of change in total energy of the electron can be expressed as (h/2π)|v₁/r₁ - nvₙ/rₙ|.

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• MatchmediumElectromagnetic Inductionfaradays law and question based on it

  List-I contains four conducting loops lying in the XY plane, as shown in the figures. The loops are rotating about Z axis passing through the point O with time period T in clockwise direction. The region x > 0 contains a uniform magnetic field B in the +z direction. List-II contains the qualitative variation of the induced current i(t) for each of these loops. Choose the option which describes the correct match between the entries in List-I to those in List-II. Image

  List 1

  1. 

  2. 

  3. 

  4. 

  5. .

  List 2

  1. 

  2. 

  3. 

  4. 

  5. 

  Options

  • Option A

    P→5, Q→4, R→1, S→3

  • Option B

    P→3, Q→2, R→5, S→4

  • Option C

    P→3, Q→2, R→1, S→4

  • Option D

    P→5, Q→1, R→2, S→3

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