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Untitled Quiz

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Questions and Answers

What is the angular velocity of the frog in the COM frame?

  • $\sqrt{\frac{2v_0}{m}}$
  • $\frac{v_0}{2m}$
  • $\frac{2v_0}{m}$
  • $\frac{v_0}{m}$ (correct)

    • What is the velocity of block B with respect to the COM frame?

  • $v_0 cos(\omega t) + v_0$
  • $-v_0 + v_0 cos(\omega t)$ (correct)
  • $v_0 + v_0 cos(\omega t)$
  • $v_0 cos(\omega t) - v_0$

    • What is the range of the frog in the ground frame?

  • $\frac{2v_0^2}{g}$
  • $\frac{6v_0^2}{g}$
  • $\frac{3v_0^2}{g}$
  • $\frac{12v_0^2}{g}$ (correct)

    • What is the time of flight of the frog in the ground frame?

    <p>$\frac{6v_0}{g}$</p> Signup and view all the answers

    What is the initial velocity of the frog in the COM frame?

    <p>$v_0$</p> Signup and view all the answers

    What is the displacement of the frog in the COM frame?

    <p>$\lambda_0 + v_0T - v_0 sin(\omega T)$</p> Signup and view all the answers

    What is the expression for λ0?

    <p>$R - v_0T + v_0 sin(\omega T)$</p> Signup and view all the answers

    What is the final expression for λ0?

    <p>$\frac{6v_0^2}{g} - v_0 \pi$</p> Signup and view all the answers

    What is the condition for the angular momentum of a system to be conserved?

    <p>The net torque acting on the system is zero</p> Signup and view all the answers

    What is the expression for the angular velocity ω after the collision?

    <p>v0/(3R)</p> Signup and view all the answers

    What is the condition for the mechanical energy to be conserved after the collision?

    <p>The system is elastic</p> Signup and view all the answers

    What is the value of v0 in terms of g and h?

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

    What is the minimum condition for the projectile to graze the cylinder?

    <p>It touches the cylinder at two points</p> Signup and view all the answers

    What is the value of ω in terms of R and g?

    <p>√(g/(3R))</p> Signup and view all the answers

    What is the change in potential energy equal to?

    <p>2x^2 - 2x + 16x</p> Signup and view all the answers

    What is the value of K at 298 K?

    <p>2.303 log (50/100)</p> Signup and view all the answers

    What is the possible transition of 3 and 4?

    <p>3 → 2 and 4 → 2</p> Signup and view all the answers

    What is the molecular mass of A2B4?

    <p>100</p> Signup and view all the answers

    What is the ratio of A to B?

    <p>1:2</p> Signup and view all the answers

    What is the value of α at 10 min?

    <p>50%</p> Signup and view all the answers

    What is the percentage of B2 at 10 min?

    <p>50%</p> Signup and view all the answers

    What is the percentage of A2 at 10 min?

    <p>25%</p> Signup and view all the answers

    What is the expression for u in terms of v and g?

    <p>u = v + 2gR(1 + cos α)</p> Signup and view all the answers

    What is the angle α for which u is minimum?

    <p>45°</p> Signup and view all the answers

    What is the relationship between u and v at the instant just after the jump?

    <p>u = 5v</p> Signup and view all the answers

    What is the expression for u^2 in terms of R and g?

    <p>u^2 = Rg(2 + 2cos^2 α)</p> Signup and view all the answers

    What type of bond is present in AlCl3?

    <p>(3C – 4e) bond</p> Signup and view all the answers

    What is the value of tan^2 θ0 in terms of R and g?

    <p>tan^2 θ0 = 3 + 2^2</p> Signup and view all the answers

    What is the expression for v^2 in terms of R and g?

    <p>v^2 = 2Rg sin α</p> Signup and view all the answers

    How many (3C – 2e) bonds are present in B2H6?

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

    What is the condition for orbitals to be degenerate in an electron system?

    <p>In a one-electron system</p> Signup and view all the answers

    What is the minimum value of u^2 in terms of R and g?

    <p>u^2 = 4Rg</p> Signup and view all the answers

    What is the relationship between u and v just before the jump?

    <p>u = v</p> Signup and view all the answers

    Which orbitals are degenerate in the second excited state?

    <p>Only three p-orbitals (2p)</p> Signup and view all the answers

    What is the value of x in Sol.x = 9, y = 3, z = 2?

    <p>9</p> Signup and view all the answers

    What is the number of (3C – 2e) bonds in the given molecule?

    <p>6</p> Signup and view all the answers

    Which element is present in the molecule BeH2?

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

    How many (3C – 2e) bonds are present in a molecule with 4-(3C-2e) bonds?

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

    Study Notes

    Conservation of Angular Momentum

    • Angular momentum of a system is conserved about the axis passing through the pivots.
    • Li (just before collision) = Lf (just after collision)
    • mv0R = (mR2 + (5m)R2)ω

    Conservation of Mechanical Energy

    • Applying conservation of mechanical energy after the collision:
      • 1/2[mR2 + (5m)R2]ω2 + mgR = 5mg
      • ω = 3R/8
      • v0 = 2gh → h = 21R/8
      • ω = √(7g/12R)

    Minimum Velocity

    • For u to be minimum, it just grazes the cylinder at two points.
    • u2 = v2 + 2gh
    • u2 = Rg(2 + 2cosα)
    • For u min, dα/d(u2) = 0 → cosα = 1/2
    • α = 45°
    • u02 = Rg(2 + 2)

    Collision and Motion

    • After the jump by the frog, v = 2v0
    • vBC = vB - vCM = v0cos(ωt)
    • ω = √(2k/m)
    • vB = vCM + v0cos(ωt)

    Projectile Motion

    • R = 2(3v0/g)
    • T = 6v0/g
    • λ0 = R - ∫vBdt
    • λ0 = R + v0T - v0sin(ωT)
    • λ0 = R + v0T - v0sin(6v0/g)

    Potential Energy

    • Change in potential energy = - mg(Rsinθ - 2x) + 2x
    • ΔPE = -14x/8 + 7x/4

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