Rotational Motion Quiz: Discs Rolling and Angular Momentum

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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?

Difference in moments of inertia Signup and view all the answers

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

Conservation of angular momentum Signup and view all the answers

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

Magnetic field strength in the cube 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?

(2 + \sqrt{2}, \sqrt{2} + 1) 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?

(1, -2) Signup and view all the answers

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

Quadrant I Signup and view all the answers

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

(\sqrt{5}, 45^\circ) 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?

$5$ units 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?

Dark 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?

Bright 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?

Shifted to the left of 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?

Dark 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?

Shifted to the right of 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?

Bright Signup and view all the answers

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

1.15 Signup and view all the answers

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

Increase the number of ejected photoelectrons Signup and view all the answers

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

$2.5 \times 10^{-2}$ m 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?

Shifts the fringes closer together 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?

Interference pattern will have narrower fringes 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?

Decrease its sliding speed Signup and view all the answers

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

4 Signup and view all the answers

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

1 Signup and view all the answers

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

$a - b heta$ Signup and view all the answers

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

$rac{1}{16}$ 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?

$1$ 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?

$2$ Signup and view all the answers