JEE Advanced 2013 physics questions with solutions

Showing 1–9 of 9 questions

• ParagraphmediumElectromagnetic Induction

  A point charge Q moves in a circular orbit of radius R in the xy-plane with angular velocity ω. This is equivalent to a steady current Qω/(2π). A uniform magnetic field along +z is switched on and increases uniformly from 0 to B in 1 s. Assume the orbital radius remains constant. The changing field induces an emf. The magnetic dipole moment of an orbiting charge is proportional to its angular momentum with constant γ.

  Sub-question 1

  The change in magnetic dipole moment associated with the orbit at the end of the magnetic-field change is:

  Options

  • Option A

    -γBQR²

  • Option B

    -γBQR²/2

  • Option C

    γBQR²/2

  • Option D

    γBQR²

  Sub-question 2

  The magnitude of the induced electric field in the orbit at any instant during the magnetic-field change is:

  Options

  • Option A

    BR/4

  • Option B

    BR/2

  • Option C

    BR

  • Option D

    2BR

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• NumericeasyNuclear physics

  A freshly prepared radioisotope has half-life 1386 s and initial activity 10³ s⁻¹. Given ln2 = 0.693, find the nearest-integer percentage of the initial nuclei that decay in the first 80 s.

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• MCQmediumUnit dimension and error

  Using the expression 2d sin θ = λ, one calculates the values of d by measuring the corresponding angles θ in the range 0 to 90°. The wavelength λ is exactly known and the error in θ is constant for all values of θ. As θ increases from 0° :-

  Options

  • Option A

    the absolute error in d remains constant

  • Option B

    the absolute error in d increases

  • Option C

    the fractional error in d remains constant

  • Option D

    the fractional error in d decreases

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• MCQmediumWork , Power and Energyconservative force and potential energy

  A particle of mass m is acted on by $\vec{F}$=K[x î+y ĵ]/(x²+y²$)^{\frac32}$. It is moved from (a,0) to (0,a) along a circular path of radius a about the origin. The work done is:

  Options

  • Option A

    2Kπ/a

  • Option B

    Kπ/a

  • Option C

    Kπ/(2a)

  • Option D

    0

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• Multi-correctmediumSimple Harmonic Motion

  A particle of mass m is attached to a massless spring of constant k on a frictionless horizontal plane. Starting from equilibrium at t=0 with velocity u₀, it collides elastically with a rigid wall when its speed is 0.5u₀. After collision:

  Select all that apply

  • Option A

    Its speed on returning to equilibrium is u₀

  • Option B

    It first passes equilibrium at t=π√(m/k)

  • Option C

    Maximum compression occurs at t=(4π/3)√(m/k)

  • Option D

    It passes equilibrium for the second time at t=(5π/3)√(m/k)

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• ParagraphmediumNuclear physics

  Binding energy is the mass-defect energy of a nucleus. A heavy nucleus can split only when the total mass of the products is smaller, and light nuclei can fuse when the final mass is smaller. Use the following neutral-atom masses (u): ¹₁H 1.007825, ²₁H 2.014102, ³₁H 3.016050, ⁴₂He 4.002603, ⁶₃Li 6.015123, ⁷₃Li 7.016004, ⁷⁰₃₀Zn 69.925325, ⁸²₃₄Se 81.916709, ¹⁵²₆₄Gd 151.919803, ²⁰⁶₈₂Pb 205.974455, ²⁰⁹₈₃Bi 208.980388 and ²¹⁰₈₄Po 209.982876. Take 1u=932 MeV c⁻².

  Sub-question 1

  When ²¹⁰₈₄Po at rest undergoes α-decay, find the α-particle kinetic energy in keV.

  Options

  • Option A

    5319

  • Option B

    5422

  • Option C

    5707

  • Option D

    5818

  Sub-question 2

  Using the given atomic masses, which statement is energetically allowed?

  Options

  • Option A

    The nucleus ⁶₃Li can emit an α-particle.

  • Option B

    The nucleus ²¹⁰₈₄Po can emit a proton.

  • Option C

    Deuteron and α-particle can undergo complete fusion.

  • Option D

    The nuclei ⁷⁰₃₀Zn and ⁸²₃₄Se can undergo complete fusion.

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• NumericmediumWork , Power and EnergyPower

  A particle of mass 0.2 kg starts from rest and moves in one dimension under a force delivering constant power 0.5 W. Find its speed after 5 s.

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• ParagraphmediumWork , Power and Energykinetic enegy and work engery theorem

  A small block of mass 1 kg is released from rest at the top of a rough circular track of radius 40 m. It slides without toppling. The work done against friction up to point Q is 150 J. Take g=10 m/s².

  

  Sub-question 1

  For the rough circular track described in the paragraph, the normal reaction at point Q is:

  Options

  • Option A

    7.5 N

  • Option B

    8.6 N

  • Option C

    11.5 N

  • Option D

    22.5 N

  Sub-question 2

  For the same rough circular track, the speed of the block at point Q is:

  Options

  • Option A

    5 m/s

  • Option B

    10 m/s

  • Option C

    10√3 m/s

  • Option D

    20 m/s

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• MCQmediumWave Optics

  In YDSE with wavelength λ, what path difference corresponds to a point having half the peak intensity?

  Options

  • Option A

    (2n+1)λ/2

  • Option B

    (2n+1)λ/4

  • Option C

    (2n+1)λ/8

  • Option D

    (2n+1)λ/16

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