Classical Mechanics-Lagrangian and Hamiltonian Formalism and Equations of Motion (CSIR Physical Sciences): Questions 8 - 10 of 11

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Question number: 8

» Classical Mechanics » Lagrangian and Hamiltonian Formalism and Equations of Motion

Appeared in Year: 2013

MCQ▾

Question

A pendulum consists of a ring of mass M and radius R suspended by a massless rigid rod of length l attached to its rim. When the pendulum oscillates in the plane of the ring, the time period of oscillation is (Dec. 2013)

Choices

Choice (4) Response

a.

2πl+Rg

b.

2πg(2R2+2Rl+l2)14

c.

2πg(l2+R2)14

d.

2π2R2+2Rl+l2g(R+l)

Question number: 9

» Classical Mechanics » Lagrangian and Hamiltonian Formalism and Equations of Motion

Appeared in Year: 2013

MCQ▾

Question

Consider a particle of mass m attached to two identical springs each of length l and spring constant k (see the figure below). The equilibrium configuration is the one where the springs are unstretched. There are no other external forces on the system. If the particle is given a small displacement along the x – axis, which of the following describes the equation of motion for small oscillations?

 A particle attached to two identical springs

a Particle Attached to Two Identical Springs

In figure a particle of mass m attached to two identical springs is shown each of length l and spring constant k.

(Dec- 2013)

Choices

Choice (4) Response

a.

mx¨+kx=0

b.

mx¨+kx3l=0

c.

mx¨kx3l2=0

d.

mx¨+2kx=0

Question number: 10

» Classical Mechanics » Lagrangian and Hamiltonian Formalism and Equations of Motion

Appeared in Year: 2011

MCQ▾

Question

A particle of mass ‘m’ moves inside a bowl. If the surface of the bowl is given by the equation z=12a(x2+y2) where, a is a constant, the Lagrangian of the particle is: (December)

Choices

Choice (4) Response

a.

12m(r˙2+r2ϕ˙2gar2)

b.

12m[(1+a2r2)r˙2+r2ϕ˙2]

c.

12m[(1+a2r2)r˙2+r2ϕ˙2gar2]

d.

12m(r˙2+r2θ˙2+r2sin2θϕ˙2gar2)

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