Paper 1 physics questions with solutions

Showing 1–10 of 16 questions

• MCQmediumRotational MotionCombined Translational & Rotational 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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• Multi-correctmediumAtomic Structure and X-raysAtomic Structure & Bohr's 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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• MatchmediumGeometrical opticsDispersion, Dispersive Power & Prism Combinations

  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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• NumericmediumSimple Harmonic MotionPhysical Pendulum, Torsional Pendulum and Superposition of SHM

  A tank contains two immiscible liquids of densities 6ρ and 2ρ. The higher density liquid is filled up to a height L/2 from the bottom. A thin rod of density ρ and length L is fully immersed and hinged at the bottom so that it can oscillate freely, as shown in the figure. If the rod is slightly disturbed from its equilibrium, the time period of small oscillations is (2π/n)√(L/g), where g is the acceleration due to gravity. The value of n is:

  

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• NumericmediumThermodynamicsThermodynamic Cycles, Heat Engines, Efficiency and 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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• MatchmediumElectromagnetic InductionMagnetic Flux,Faraday's Laws of Electromagnetic Induction and Lenz's Law

  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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• MCQmediumElectromagnetic InductionMutual Inductance, L-C Oscillations and Transformers

  Consider a circuit consisting of a capacitor of capacitance C and a coil with N turns per unit length, cross sectional area S and length d, where d² ≫ S. There is another coil of length d/2, cross sectional area S/2 and 2N turns per unit length completely inside the larger coil, as shown in the figure. The ends of this smaller coil are connected with each other by an insulated conducting wire. The self-inductance of the larger coil is L. Neglecting edge effects and all the Ohmic resistances, the resonant frequency of the circuit is:

  

  Options

  • Option A

    4/√(15LC)

  • Option B

    6/√(5LC)

  • Option C

    2/√(3LC)

  • Option D

    √[2/(3LC)]

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• MatchmediumRotational MotionMoment of Inertia & Rotational Kinetic Energy

  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-correctmediumKinematics part-2 Projectile MotionMotion in 2-D and ground to ground projectile

  A particle is thrown with a speed v from a point O at an angle θ with the horizontal plane such that it passes through the point P at a height of 1 m and horizontal distance of 5 m from O, as shown in the figure. If acceleration due to gravity is g m s⁻², then the correct statement(s) is/are:

  

  Select all that apply

  • Option A

    If θ = 45°, then v = 5√g/2 m s⁻¹.

  • Option B

    If θ = 45°, the particle reaches its maximum height before it reaches P.

  • Option C

    If θ = 30°, the particle reaches its maximum height after reaching P.

  • Option D

    If θ = tan⁻¹(1/5), then v = 125√g m s⁻¹.

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• NumericmediumMagnetic effect of currentMagnetic Field Produced by Moving Charges

  A hollow, right circular cone of base radius R and height h, with its tip at the origin is rotating about the Z-axis with an angular velocity ω, as shown in the figure. The cone carries a total charge Q uniformly distributed on its curved surface. The magnitude of magnetic field at a point (0,0,z), where z ≫ R and z ≫ h, is n μ₀QR²ω/(4πz³). The value of n is:

  

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