Untitled Quiz

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson
Download our mobile app to listen on the go
Get App

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

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

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

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

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

What is the expression for λ0?

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

What is the final expression for λ0?

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

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

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

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

<p>2gh (A)</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 (D)</p> Signup and view all the answers

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

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

What is the change in potential energy equal to?

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

What is the value of K at 298 K?

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

What is the possible transition of 3 and 4?

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

What is the molecular mass of A2B4?

<p>100 (D)</p> Signup and view all the answers

What is the ratio of A to B?

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

What is the value of α at 10 min?

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

What is the percentage of B2 at 10 min?

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

What is the percentage of A2 at 10 min?

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

What is the angle α for which u is minimum?

<p>45° (A)</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 (B)</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) (B)</p> Signup and view all the answers

What type of bond is present in AlCl3?

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

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

<p>Two (B)</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 (C)</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 (B)</p> Signup and view all the answers

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

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

Which orbitals are degenerate in the second excited state?

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

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

<p>9 (A)</p> Signup and view all the answers

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

<p>6 (B)</p> Signup and view all the answers

Which element is present in the molecule BeH2?

<p>Beryllium (C)</p> Signup and view all the answers

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

<p>4 (B)</p> Signup and view all the answers

Flashcards are hidden until you start studying

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

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

Related Documents

FIITJEE JEE (Advanced) 2023 Past Paper PDF - Part 1 - Paper 2

More Like This

Use Quizgecko on...
Browser
Open
Browser
Browser