41. A particle constrained to move along the X-axis in a potential V = kx2, is subjected to an external time dependent force $$\overrightarrow {\bf{F}} \left( t \right).$$ Here, k is a constant, x, the distance from the origin and t is the time. At some time T, when the particle has zero velocity at x = 0, the external force is removed. The particle will
42. A system of four particles is in X-Y plane of these two particles of masses m are located at (1, 1) and (-1, 1). The remaining two particles each of mass 2m are located at (1, 1) and (-1, -1). The xy component of moment of inertia tensor of the system of particles is
43. A particle of mass m is constrained to move on the plane curve xy = c (c > 0) under gravity (Y-axis vertical). The Lagrangian of the particle is given by
44. An electron gains energy so that its mass becomes 2m0. Its speed is
45. Let (p, q) and (P, Q) be two pairs of canonical variables. The transformation Q = qα cos βp, P = qα sin βp is canonical for
46. Two bodies of masses m and 2m are connected by spring constant, the frequency of normal mode is
47. A heavy symmetrical top is rotating about its own axis of symmetry (Z-axis). If $${I_1},\,{I_2}$$ and $${I_3}$$ are the principal moments of inertia along X, Y and Z axes respectively then
48. A hoop is pivoted at a point on circumference. The period of small oscillations in the plane of loop is
49. The Lagrangian of a system is given by $$L = \frac{1}{2}{\dot q^2} + q\dot q - \frac{1}{2}{q^2}$$
It describes motion of a
It describes motion of a