Derive an expression for intermodal dispersion for a multimodal step-index fibre.
cse-2012-subject-02-007
A diffraction grating of width 5 cm with slits of width 10^{-4} cm separated by a distance of 2\times10^{-4} cm is illuminated by light of wavelength 550 nm. What will be the width of the principal maximum in the diffraction pattern? Would there be any missing orders?
cse-2012-subject-02-006
Distinguish between Fresnel and Fraunhofer classes of diffraction. Show that the area of each Fresnel half-period zone is same.
cse-2012-subject-02-005
Two identical relativistic particles of rest mass m and kinetic energy T collide head-on. What is the relative kinetic energy, i.e., the kinetic energy T' of one in the rest frame of the other?
cse-2012-subject-01-006
Define a conservative field. Determine if the field given below is conservative in nature: \vec{E}=c\left[y^2\hat{i}+(2xy+z^2)\hat{j}+2yz\hat{k}\right]\,\mathrm{V/m} where c is a constant.
cse-2012-subject-01-001
Consider a uniform half-sphere of radius R and mass M. The half-sphere is supported by a frictionless horizontal plane as shown in the figure. The half-sphere lies in the region z<0.
Find the centre of mass of the half-sphere.
cse-2012-subject-01-002
A particle is moving in a central force field on an orbit given by r = ke^{\alpha\theta}, where k and \alpha are positive constants, r is the radial distance and \theta is the polar angle.
(i) Find the force law for the central force field.
(ii) Find \theta(t).
(iii) Find the total energy.
cse-2012-subject-01-003
A rigid body is spinning with an angular velocity of 4\ \mathrm{rad\,s^{-1}} about an axis parallel to the direction (4\hat{\jmath}-3\hat{k}) passing through the point A with \overrightarrow{OA}=2\hat{\imath}+3\hat{\jmath}-\hat{k}, where O is the origin of the coordinate system. Find the magnitude and direction of the linear velocity of the body at point P with \overrightarrow{OP}=4\hat{\imath}-2\hat{\jmath}+\hat{k}.
cse-2012-subject-01-004
Calculate the moment of inertia of a solid cone of mass M, height h, vertical half-angle \alpha and radius of its base R, about an axis passing through its vertex and parallel to its base.
cse-2012-subject-01-005
A projectile of mass M explodes, while in flight, into three fragments. One fragment of mass m_1=M/2 travels in the original direction of the projectile. Another fragment of mass m_2=M/6 travels in the opposite direction and the third fragment of mass m_3=M/3 comes to rest. The energy E, released in the explosion, is 5 times the kinetic energy of the projectile at explosion. What are the velocities of the fragments?
cse-2012-subject-01-007
A man has a mass of 100\text{ kg} on earth. When he is on the space craft an observer from the earth registers his mass as 102\text{ kg}. Determine the speed of the space craft.
ifos-2012-subject-01-006
Using the concept of the operator equation for a given vector quantity of a rotating body, show that \vec{v}_s = \vec{v}_r + \vec{\omega} \times \vec{r} where \vec{v}_s and \vec{v}_r are the velocities of the particle relative to space and rotating sets of axes while \vec{\omega} is the angular velocity of the earth relative to the inertial system. Obtain the expression for the Coriolis force for such a moving system of mass m.
ifos-2012-subject-01-005
State Hamilton's principle for the motion of a monogenic system. Use the calculus of variation to deduce Lagrange's equation that follows from Hamilton's principle. Explain carefully all the terms used in the derivation.
ifos-2012-subject-01-004
Using D'Alembert's principle, show that the following relation can be obtained for a system of particles under generalized coordinates \sum_i \vec{F}_i \cdot \delta \vec{r}_i = \sum_j Q_j \delta q_j with Q_j = \sum_i \vec{F}_i \cdot \frac{\partial \vec{r}_i}{\partial q_j}. What is the significance of Q_j ?
ifos-2012-subject-01-003
Starting with Newton's second law of motion, establish D'Alembert's principle and discuss its significance.
ifos-2012-subject-01-002
Express Lagrange's equation of motion for the cyclic coordinate q_j and show that the result leads to the general conservation theorem for the generalized momentum coordinates.
ifos-2012-subject-01-001
Draw the common-base amplifier circuit, using an n-p-n transistor and briefly discuss its working.
cse-2011-subject-08-007
An electron beam of 4 Kev is diffracted through a Bragg angle of 16^\circ for the first maxima. If the energy is increased to 16 keV, find the corresponding Bragg angle for diffraction.
cse-2011-subject-08-002
Using band theory of solids, explain whether the effective mass of an electron can be positive, negative as well as infinity. Explain the significance of negative mass.
ifos-2011-subject-08-002
(i) What are intrinsic and extrinsic semiconductors ? Explain. (ii) How are n-type and p-type semiconductors obtained ?
ifos-2011-subject-08-003