A particle is scattered by a rigid sphere of radius R , as given in the figure. Determine the differential scattering cross-section and the total scattering cross-section.

A particle moves under a central force,  . Is this an attractive or a repulsive force? Find the radius and energy of the circular orbits.

Using Cauchy’s residue theorem, evaluate the integral

The kinetic and potential energies for a mechanical system with two generalized coordinates q₁ and q₂ are 

i) Write down the Lagrangian for the system.

ii) Obtain the expressions for the generalized momenta.

iii) Derive the Euler Lagrange equations of motion for the system.

iv) Obtain the energy function for the system.

Show that the vectors  are linearly independent.

Using the D' Alembert’s Principle determine the equation of motion for an Atwood’s machine with masses M and 3M

Write down the equations of constraint/s for the following systems and classify them as holonomic/nonholonomic and scleronomic/rheonomic:

i) a particle of mass m sliding down the surface of a sphere of radius R without friction, under the action of gravity.

ii) a simple pendulum of length L for which the point of support is oscillating vertically with an angular speed   and amplitude A.

Show that g^ij is a contravariant tensor of rank 2.

A particle of mass m moving to the right with an initial velocity u collides elastically with a particle of unknown mass M coming from the opposite direction. After the collision m has a velocity u/2 at right angles to the incident direction, and M is deflected back making an angle of 45 degrees to its incident direction as shown below. Calculate the ratio M/m.

Diagonalized the matrix:

The eigenvalues of A are: λ₁ = 2, λ₂  =1 and λ₃ = -1.

Obtain the eigenvalues and the corresponding eigenvectors of the matrix:

Using the generating function, establish the relation between H_n (x) and H_n (-x). 

Using the recurrence relation, show that

भेद प्रवर्धक प्रकार के EVM की संरचना एवं कार्य समझाएं।

D-फ्लिप फ्लॉप का कार्य समझाएं। इसके और D-लैच के बीच अंतर बताएं।

Using recurrence relation, show that

where J_n(x) is the Bessel function of the first kind. 

एक 4-बिट वाले DAC की निर्गम वोल्टता 1011 निवेश के लिए 22 mV है। इस DAC का वियोजन कितना होगा? 0101 निवेश के लिए V_out मालूम करें।

Mod-6 गणित्र डिज़ाइन करें और इसका परिपथ चित्र खींचें।

IC LM 317 का प्रयोग करके 30V निर्गम देने वाला वोल्टता नियंत्रक डिज़ाइन करें और इसका परिपथ चित्र खींचें।

IC 380 का प्रयोग करके 50 लब्धि वाले प्रवर्धक का परिपथ चित्र खींचें। निवेश सिग्नल को अप्रतिलोमी निवेश पर लागू करें।