Classical Mechanics (GATE Physics): Questions 16 - 18 of 38

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Question number: 16

» Classical Mechanics » Lorentz Transformations

Appeared in Year: 2014

MCQ▾

Question

Which one of the following quantities is invariant under Lorentz transformation?

Choices

Choice (4) Response
a.

Charge

b.

Electric field

c.

Charge density

d.

Current

Question number: 17

» Classical Mechanics » Lagrange's and Hamilton's Formalisms

Appeared in Year: 2014

MCQ▾

Question

The Hamilton’s canonical equations of motion in terms of Poisson Brackets are –

Choices

Choice (4) Response
a.

q˙={H,p};p˙={H.q}

b.

q˙={H,q};p˙={H,P}

c.

q˙={q,H};p˙={p.H}

d.

q˙={p,H};p˙={q,H}

Question number: 18

» Classical Mechanics » Relativistic Kinematics

Appeared in Year: 2014

MCQ▾

Question

A bead of mass m can slide without friction along a massless rod kept at 45° with the vertical as shown in the figure. The rod is rotating about the vertical axis with a constant angular speed ω . At any instant, r is the distance of the bead from the origin. The momentum conjugate to r is –

Ellipse c Ellipse c: Ellipse with foci F, G passing through HAngle? Angle? : Angle between E, D, JSegment f Segment f: Segment [I, J] Segment g Segment g: Segment [L, M] Vector u Vector u: Vector [D, E] Vector u Vector u: Vector [D, E] Vector u_1 Vector u_1: Vector [D_1, E_1] Vector u_1 Vector u_1: Vector [D_1, E_1] Vector v Vector v: Vector [N, O] Vector v Vector v: Vector [N, O] Vector w Vector w: Vector [P, Q] Vector w Vector w: Vector [P, Q] Point M Point M: Point on fPoint M Point M: Point on f45? text1 = “45? “? text1_1 = “? “/hat {z} text1_2 = “/hat {z} “/hat {z} text1_2 = “/hat {z} “m text1_3 = “m”r text1_4 = “r”/hat {x} text1_5 = “/hat {x} “/hat {x} text1_5 = “/hat {x} “

Motion of a Bead at 45 With Vertical

Figure shows that a bead of mass m can slide without friction along a massless rod kept at 45 with the vertical as shown in the figure.

Choices

Choice (4) Response
a.

12mr˙

b.

mr˙

c.

12mr˙

d.

2mr˙

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