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Three point masses are connected by three <> springs with spring constant ‘k’. The
number of degrees of freedom of the system is :
(8) 9 (B) 6 (© 8 (D) 9-ಓ

In the case of a simple pendulum, the Lagrangian is given by L=mi20%+mg! ೧೦58, The
angular acceleration of the bob will be :

ಟು ೨8 ® -3 coso © + ८७ (0) -ತೆ ‏ممه‎

A particle of mass ‘m’, charge 'q’ and linear momentum ‘P’ enters an electromagnetic field of
vector potential “A” and scalar potential ¢. The Hamiltonian of the particle is :

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) im[i € 8 8 7 7
2 2

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In the case of two coupled pendula of mass ‘m’ and length ‘I’ connected to a massless spring

having spring constant ‘K, the resonant frequencies are | A .

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உரக வந்த்‌ உக வந

A nucleus emits a gamma ray photon of frequency 2. The loss of internal energy by the
nucleus is 2

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1! "ಗಾ" 15 1116 rest mass of electron, the relativistic mass approaches _as the velocity
of electron approaches velocity of light.

(ಗಿ) മണ്ട B ജു ‏ا‎ டி (D) infinity

Ifa function ‘F’ does not depend on time and is a constant of motion, its Poisson bracket with
‏رام‎ vanishes.

(வ) Hamiltonian (8) Jacobian (ಲ) Lagrangian (D} D’Alembertian

is ഒ geometrical object or set with non-integral dimensions which exhibits the
property of self similarity.
(ಡಿ) Chaos (8) Fractal
(C) Attractor (D) Lyapunov exponent

126/2014 4 A