Rotational Motion Quiz: Discs Rolling and Angular Momentum
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Questions and Answers

What does the equation A = (2α1R1 + α2R2)iˆ - (ω12R1 + 1)jˆ/(R1 + R2) represent in the context provided?

  • Linear acceleration of the upper disc (correct)
  • Linear velocity of the upper disc
  • Angular velocity of the upper disc
  • Angular acceleration of the upper disc
  • What does KE of the upper disc = 4ρ(3ω12R12 + 2ω22R22 + 4ω1ω2R1R2) represent in the context provided?

  • Rotational kinetic energy of the upper disc (correct)
  • Potential energy of the upper disc
  • Linear kinetic energy of the upper disc
  • Total mechanical energy of the upper disc
  • What does L upper disc about O = m(ω1R12 + ω2R22 + ω1ω2R1R2)(−k)2 represent in the context provided?

  • Angular momentum of the upper disc about O (correct)
  • Torque acting on the upper disc
  • Angular momentum of the upper disc about C
  • Angular momentum of the lower disc about C
  • In the provided context, why is L upper disc about A ≠ L disc about C?

    <p>Difference in moments of inertia</p> Signup and view all the answers

    What is the significance of PA = PC = R12 ω2, α2 in the context provided?

    <p>Conservation of angular momentum</p> Signup and view all the answers

    What does B = (2iˆ - 3jˆ + k) represent in the context provided with a mass of 50gm?

    <p>Magnetic field strength in the cube</p> Signup and view all the answers

    If a particle moves 2 units along the line x + y = 1, what is the new position of the particle?

    <p>(2 + \sqrt{2}, \sqrt{2} + 1)</p> Signup and view all the answers

    If a particle moves 5 units along the line x - 2y = 4, what is the new position of the particle?

    <p>(1, -2)</p> Signup and view all the answers

    In which quadrant is the new position of the particles located if they both move towards increasing y?

    <p>Quadrant I</p> Signup and view all the answers

    What are the coordinates of the point (2, -1) in polar form?

    <p>(\sqrt{5}, 45^\circ)</p> Signup and view all the answers

    If one particle moves 3 units along x-axis and the other moves 4 units along y-axis, what will be the distance between them?

    <p>$5$ units</p> Signup and view all the answers

    If strip A is placed over one slit and strip B over the other, what will be the order of the fringe at point P?

    <p>Dark</p> Signup and view all the answers

    If strip C is placed over both slits, what will be the order of the fringe at point P?

    <p>Bright</p> Signup and view all the answers

    If strip A is placed over one slit and strip C over the other, what will be the order of the fringe at point P?

    <p>Shifted to the left of P</p> Signup and view all the answers

    If strip B is placed over both slits, what will be the order of the fringe at point P?

    <p>Dark</p> Signup and view all the answers

    If strip A is placed over one slit, what will be the order of the fringe at point P?

    <p>Shifted to the right of P</p> Signup and view all the answers

    If no strip is placed over the slits, what will be the order of the fringe at point P?

    <p>Bright</p> Signup and view all the answers

    What is the value of 'n' in the given scenario?

    <p>1.15</p> Signup and view all the answers

    If the light wavelength is changed to 2000 Å, what effect would it have on the photoelectrons ejected?

    <p>Increase the number of ejected photoelectrons</p> Signup and view all the answers

    What is the radius of the path followed by electrons ejected from the plate with maximum energy?

    <p>$2.5 \times 10^{-2}$ m</p> Signup and view all the answers

    How does the introduction of a glass slab in front of one of the slits in a YDSE experiment affect interference patterns?

    <p>Shifts the fringes closer together</p> Signup and view all the answers

    If water is replaced with a liquid having a higher refractive index, what will happen to the YDSE interference pattern?

    <p>Interference pattern will have narrower fringes</p> Signup and view all the answers

    How would neglecting viscosity affect the behavior of petrol considered as a solid semi-cylinder inside a tank wagon?

    <p>Decrease its sliding speed</p> Signup and view all the answers

    What is the smallest value of $P(A igcap B^c)$?

    <p>4</p> Signup and view all the answers

    In the context provided, what value does the definite integral $4igint f(x) dx$ equal to?

    <p>1</p> Signup and view all the answers

    If $f(x) = rac{1}{e^x}$, what is the value of the definite integral $igint_0^1 e^x + 8 dx$?

    <p>$a - b heta$</p> Signup and view all the answers

    If $G(x) = rac{1}{g(x)}$ and $f(4) = 2$ with $f'(4) = 16$, what is $(G'(2))^2$?

    <p>$rac{1}{16}$</p> Signup and view all the answers

    In the context provided, if $f(x) = rac{1}{x - r}$, what is the definite integral $igint_{r=1} f(x)dx$ equal to?

    <p>$1$</p> Signup and view all the answers

    What value does $igint t imes f(2x - t) dt = tan^{-1}(x^2)$ represent in the provided context?

    <p>$2$</p> Signup and view all the answers

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