Consider a particle of mass m moving in a one dimension under a force with the potential V ( x ) = a x^{3}  3xl). where the constant k > 0. The frequency of a small amplitude oscillation of the panicle about the equilibrium position
If the functions G and F depends on the position coordinates q_{i} momenta p_{i} and time t, then poisson bracket of G and F is defined as
Then [G,p_{r}] (Here r is arbitrary number)
1 Crore+ students have signed up on EduRev. Have you? Download the App 
Two forces are given below in spherical polar and cartersian coordiantes
Where A, B and R are constants. Then
The Lagrangian of a particle is
where k is a positive constant, q_{1} and q_{2} in generalised coordinates. The equation of motion are
Let (p.q) and (P, Q) be two pairs of canonical variables. The transformation P q cot βp and is canonical for β = nα. The value of n is_______
The mass of a particle is measured to be √2 times of its rest mass. The ratio of kinetic energy and total energy is ____________ (up to two decimal places)
The percentage contraction of a rod moving with a velocity 0.8 c in a direction inclined at 60° to its own length ______% (up to one decimal place)
The Hamiltonian of a particle with mass m =1/2 units moving along xaxis inside a potential V(x) = e^{x }is given by H = p^{2} + e^{x} Assume p> 0. The phase space trajectory of the particle will be
In a central force field, the trajecting (in plane polar cooridantes) of a particle is given by where m is the mass of the particle. L is angular momentiun and e is the eccentricity of the particle's motion. Whcih one of the following conditions given rise to circular trajectory?
The minimum value of coefficient of friction for an inclined plane of angle θ = 45^{0} in order that a hoop will roll down without slipping is______(Upto one decimal place)
A distant galaxy is observed to have its hydrogen β line shifted to a wavelength of 580 nm, away from the laboratory value of 434 mn. The approximate velocity of recession of the distant galaxy is
Two balls, of mass m and mass 2m. approach from perpendicular directions with identical speeds and collide. After the collision, the more massive ball moves with the same speed v but downward, perpendicular to its original direction. The less massive ball moves with speed U at an angle θ with respect to the horizontal. If no external forces act during the collision then the final speed of less massive ball is αv. The value of α is_______ (up to 1 decimal place)
The orthogonal trajectories to the curve x^{2} + (y1)^{2} = 1 are a family of
Consider a charged sphere of radius R with charge density f(r ) = e^{r}. The gradient vector to the family of equipotential surfaces of this charged surface points
The value of the integral over a contour of unit circle centered at origin. (Taken in the anticlockwise sense) is_______(Answer should be an integer)
Given the value of H_{5}(0 ) is _________ (Answer should be an integer)
Which one of the following combinations can be a possible set of eigenvalues for a 4 x 4 unitary matrix?
Consider a complex function f(x. y) = e^{ax} + i In by. If the function is analytic at (0. 1) then the possible values of (a, b) is
If δ(x) is the DiracDelta function. and x has the dimension of angular momentum, then δ(x) has a dimension which can be written as [L^{α}M^{β}T^{y}]. The value of (α,β,γ) is
The value of Trace ______ where is the pauli matrix (upto 2 decimal places)
Consider a vector The line integral over the contour as shown is equal to _____ (upto 2 decimal places)
Given below are forces in Cartesian and spherical coordinates. Which of the following are conservative?
A particle of m moves with speed v. Ail explosion divides the particle into two half, giving each half a speed V in the centre of mass frame. Assume all motion is confined to one dimension. The increase in kinetic energy in the Lab frame is
A particle is thrown from earth's surface with speed where M and R are mass and radius of the earth respectively. The trajectory of the particle will be a /an
A cricular disc is rotaing about an axis, shown in figure, makes an angle θ = 30^{0} with the vertical axis. The moment of inertia of the disc about that axis is
A block of mass M with the shape of an inverted trapezoid is pushed downwards minimum force required to tip the block is
An electron moves in the lab with a speed of 0.6c. An observer moves with a velocity of 0.8 c along the direction of the motion of the electron. The kinetic energy of the electron as determined by the observer is _____ MeV (Upto three decimal places)
The relativistic Lagrangian of a point particle moving in 1 D is given by
Here m is mass of particle and c is speed of light. The graph of x vs t is a
For a dynamical system, time evolution of dynamical variable is given by
Which one of the following statement is correct?
The lagrangian of a system with one degree of freedom is given by L = 2x^{2} + 3x^{2}. If p_{x }denotes the canonical momentum conjusate to x and if is the Hamiltonium then which anions the following statements is correct?
The spacetime coordinates of two events as measured by oserver O are and The spatial separation of the two events as measured by O'. where the two events occur simultaneously ______ x 10^{4}m. (Upto three decimal places)
A three particle system consists of masses m. and coordinates (x. y. z) as follows
If L_{ij} represents the elements of moment of inertia tensor then value of ( Up to two decimal places)
A particle of mass m moves wider the action of a central force whose potential energy is U(r) = kr^{6} , k > O. If the orbit be a circle of radius a about origin, then the total energy is ηka^{6}. The value of η is _______.
A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is propertional to t^{β} . The value of β is ____________ .
Consider the following function:
which repeats itself outside the interval [5. 5]. In the Fourier series expansion of the fraction, the Fourier coefficient b_{1oo} will be equal to ________ (Symbols have their usual meanings)
Consider a complex function Which of the following is true regarding f(z)?
For which of the following functions, Fourier series expansion is not possible in the given interval?
Suppose we have differentiation equation.
with boundary condition,
Which of the following relations between y and x is correct.
Let be the Pauli matrices and Then the coordinates are related as follows:
Consider the two equations How many simultaneous real solutions does this pair of equations have?
Given a function f(x,y,z) = xyz. The magnitude of rate of change of f(x,y,z) along the direction of the vactor at a point (2, 1, 1) is ____ (upto 2 decimal places).
Consider the integral where P is a real constant. This integral has a real, nonsingular value if and only if and only if P → α. Then, α is ______.
Consider a 2 x 2 matrix A, whose characteristic equation is given by 2A^{2}  5 A + 2I = 0 . Then, the value of 2(Tr A)3(det A) = ___________
The number of nodes in the solution of the differential equation
The matrix can be related by a similarity transformation to the matrix
1 docs34 tests

1 docs34 tests
