For a system with one degree of freedom, hamiltonian is The shape of xt graph for the particle is
A particle of charge q and rest mass m_{0 }is kept at rest at the origin. A constant uniform electric field, starts acting on it at t = 0. The speed of the particle at time t is (in the following c is speed of light)
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The Lagrangian of a system is
Which one of the following is conserved?
A pendulum consists of a mass m and a massless stick of length l. The pendulum support oscillates horizontally with a position given by x (t) = (see figure). The momentum conjugate to θ is
If the Hamiltonian of a system with two degrees of freedom is given by
then the quantity that is conserved is
The Poisson bracket with a and b as constants is equal to
A particle of effective mass m is acted on by a potential energy given by
where, u_{0}, a and b are positive constants, then
The number of degrees of freedom of two particles moving on a space curve and having constant distance between them, is ______.
The average lifetime of a π meson in its own frame of reference is 26.011s. If the π  meson moves with speed 0.95c with respect to the earth, then the average distance it travels before decaying as measured byan observer at rest on Earth is approximately close to _______________________ meters (nearest integer)
A particle of mass m is subjected to a central force given by the potential The radius of the circular orbit for a particle with angular momentum, The value of η is ______.
The path of a particle of mass m moving minder some potential V ( r ) is given by the r = A exp (aθ). where A and a are constants. The form of V(r) is (in the following L and E are angular momentum, and total energy, respectively)
A system with one degree of freedom has Lagrangian, The equation of x(t) under the initial conditions t = 0, x = 0, p = mv_{0}, is
The dynamics of a particle moving on the real line is determined by the Hamiltonian
where μ and λ are constants. Then the value of dp/dq is
Hamiltonian of a one dimensional dynamical system is given by
The Poisson bracket {p, H} is equal to
For a charged particle of mass m and charge e in a magnetic field the Lagrangian is
The corresponding Hamiltonian is
Given that the linear transformation of a generalized coordinate q and corresponding momentum p,
is canonical, the value of the constant β is ______ (Here, i = √1)
Two events in a inertial referance frame separated by a distance 3.6 x 10^{8}m and occur 2s apart. The proper time interval between the occurrence of these two events is _____ sec. (upto one decimal place)
The moment of inertia of a square frame of side length a and mass M about an axis passing through one of its
comers and perpendicular to its plane is βMa^{2}. The value of β is________(upto two decimal places)
Ail object of mass m = 100 kg and volume V= 0.18 m^{3} is dropped from a height h = 100m above the surface of the water. Upon entering water (β= 1000 kg/m^{3} ), the object experiences a resistance force given by F = kv. where k = 10N sec in. The maximum depth to which the object will sink before starting to rise again is _____ m. (Neglect air resistance and assume the object looses negligible energy when going through the surface of the water). (Nearest integer)
A star receding from the earth at a speed of 5 x 10^{3}c. The wavelength shift for the sodium D_{2} line is approximately equal to ____ (nearest integer)
1 docs34 tests

1 docs34 tests
