LEADS College Defense Road Campus Time Allowed: 3 hours Paper A Max.Marks:50
Attempt any FIVE questions in all, selecting at least TWO questions from each section. All questions carry equal marks (Section -1) 1(a) what is meant by divergence of the vector field? Show that ������ �� = ��. �� where V is a vector field in three dimension ? (5) 1b) if ��(��, ��, ��) = 3�� 2 + 4�� 3 + �� 2 is a scalar field find the �������� ���� �� at point (1,-2, 3)? (5)
2(a) Define elastic and inelastic collisions. Derive expressions for the final velocities of two particles having elastic collisio n on a straight line and discuss any of two particular cases (1 +4+2) 2(b) An object of mass 2 kg makes an elastic collision with another object at rest a nd continues to move in the original direction but with one-fourth of its original speed. What is the mass of the struck particle? (3) 3(a) What is a conservative field? Prove that the gravitational force is negative derivative of the gravitational potential energy. (5+1) 3(b) What minimum initial speed must a projectile have at the Earth’s surface if it is to escape from the Earth? Ignore air friction and rotation of Earth. (4) 4(a) Define rotational inertia of a rotating body and find the rotational inertia of a solid rod about an axis through the center and perpendicular to its length. (1+6) 4(b) Derive a relation for the KE of a wheel rolling without slipping on a level surface. (3) 5(a) Discuss consequences of LORENTZ transformation for relativity of time and relativity of length (1+3+3) 5(b) what is the momentum of proton moving at a speed 0.9C? 6(a) Write a brief note on any two of the following (5+5) 1. 2. 3. Conical pendulum Surface Tension Parallel Axis Theorem (4)
7(a)Discuss the combination of two simple harmonic oscillations in the formation of Lissajous figures under typical phase and amplitude conditions in case of equal frequencies ? (7) 7(b) A 3.94 Kg block extends a spring to 15.7 cm. the block...
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