Classical Mechanics (GATE Physics): Questions 19 - 20 of 79

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Question number: 19

» Classical Mechanics » Conservation Laws

Appeared in Year: 2015

MCQ▾

Question

A particle with rest mass M is at rest and decays into two particles of equal rest masses Equation , which move along the Z – axis. Their velocities are given by,

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation

Question number: 20

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

Appeared in Year: 2012

MCQ▾

Question

A particle of mass Equation is attached to a fixed point Equation by a weightless inextensible string of length Equation . It is rotating under the gravity as shown in the figure.

Ellipse c Ellipse c: Ellipse with foci C, D passing through EArc d Arc d: CircularArc [P, Q, R] Segment f Segment f: Segment [F, G] Segment g Segment g: Segment [H, I] Vector u Vector u: Vector [A, B] Vector u Vector u: Vector [A, B] Vector v Vector v: Vector [J, K] Vector v Vector v: Vector [J, K] Vector w Vector w: Vector [L, M] Vector w Vector w: Vector [L, M] Vector a Vector a: Vector [N, O] Vector a Vector a: Vector [N, O] Vector a Vector a: Vector [N, O] Point G Point G: Point on uPoint G Point G: Point on uPoint J Point J: Point on cPoint J Point J: Point on cPoint Q Q = (5.8, 3.7) Point Q Q = (5.8, 3.7) Point R R = (5.52, 2.42) Point R R = (5.52, 2.42) ? text1 = “? “Z text1_1 = “Z”a text1_2 = “a”m text1_3 = “m”g text1_4 = “g”O text1_5 = “O”

a Particle Rotates About Z – Axis

In figure a particle of mass m, is attached to a fixed point O by a weightless inextensible string. And this particle rotating about Z – axis.

The Lagrangian of the particle is,

Equation

Where, Equation and Equation are the polar angles.

The Hamiltonian of the particle is,

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation

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