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clasical physics

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Brijmohan
Banaras Hindu University (BHU), Varanasi
PhD Condensed matter Physics
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Que.1 The Lagrangian of a particle of mass m moving in a central potential U(r) is 1) is a cyclic coordinate 3) is cyclic coordinate 2) and are cyclic coordinate 4) r is cyclic coordinate. Que.2 If a generalized coordinate q is ignorable or cyclic in a Lagrangian L, then following is conserved. 1) 3) 2) 4) ( ) Que.3 The potential energy of a simple pendulum consisting of a bob of mass m attached to a string of length l displaced from the vertical by an angle and allowed to oscillate (assume the potential energy is zero at the rest position) will be : 1) 2) 1 (ml2 2 ) mglcos 2 3) 2mglsin2 /2 ml 2 2 1 4) 2 1 Que.4 If the Lagrangian of a particle moving in one dimension is given by = 2 2 ( ) , the Hamiltonian is 1) 2) 2 1 3) 2 + ( ) xp2 + V(x) 2 2 2 2 ( ) 4) 2 + ( ) Que.5 The Hamiltonian of a system is independent of coordinate q and is given by = 4 where a is a constant. The corresponding L is 1) 1 2 - ap4 3) = 2 2 - ap4 2) L = a 4 4) 3 4 (4 ) Que.6 The Lagrangian of a particle of mass m moving in one dimension is given by = 1 2 m 2 bx, where b is the positive constant. The coordinate of the particle x (t) at time t is given by (in the following c1 and c2 are constant) 1) 2 2 + 1 + 2 2) 1 cos + 2 sin 3) 1 + 2 4) 1 cosh + 2 sin 1 1 Que.7 Lagrangian of a system is = (2 2 2 2 ) where , m and k are positive constants. Equation of motion of the system is 1) - + 2) + + 4) - - 3) + - Que.8 Lagrangian of a system is = ( 2 2 ), Hamiltonian of the system is 1) 2 + 2 2) 2 4 + 2 3) 4) 2 2 2 2 + 2 2 2 2 Que.9 If the Lagrangian of a system is = 1 2 - V(x), Hamiltonian of the system is 1) 2) 2 2 + V(x) 2 1 2 2 2 + + V(x) 3) 4) + 2 1 2 Que.10 If 1 = + 2 + 3 and 2 = 2 + (2 + 2 ) + 2 , then 1) Both are impossible electrostatic field 3) Both are possible electrostatic field 2) Only 1 is possible electrostatic field 4) Only 2 is possible electrostatic field Que.11 Find Hamiltonian of the following system 1) 2) 3) 4)

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