37 (a) (4)
(c) (2)
(d) (3)
(Mains 2010)
(1) Centre of gravity (C. G) of a body is the
point at which the weight of the body acts
(2) Centre of mass coincides with the centre of
gravity if the earth is assumed to have infinitely
large radius.
(3) To evaluate the gravitational field intensity
due to any body at an external point, the entire
mass of the body can be considered to be
concentrated at its C. G
(4) The radius of gyration of any body
rotating about an axis is the length of the
perpendicular dropped from the C. G. of the
body to the axis.
Which one of the following pairs of
statements is correct?
(a) (4) and (1)
(b) (1) and (2)
(c). (2) and (3)
(d) (3) and (4)
(Mains 2010)
The figure shows elliptical orbit of a planet m
about the sun S. The shaded area SCD is twice
the shaded area SAB. If t, is the time for the​

Consider the particle-in-a-box problem in 1d. a particle with mass m is confined to move freely between two hard walls situated at x = 0 and x = l. the potential energy function is given as (a) describe the boundary conditions that must be satisfied by the wavefunctions ψ(x) (such as energy eigenfunctions). (b) solve the schr¨odinger’s equation and by using the boundary conditions of part (a) find all energy eigenfunctions, ψn(x), and the corresponding energies, en. (c) what are the allowed values of the quantum number n above? how did you decide on that? (d) what is the de broglie wavelength for the ground state? (e) sketch a plot of the lowest 3 levels’ wavefunctions (ψn(x) vs x). don’t forget to mark the positions of the walls on the graphs. (f) in a transition between the energy levels above, which transition produces the longest wavelength λ for the emitted photon? what is the corresponding wavele

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