Mechanics Paper
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)
(Section-2)
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 is
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)
(Section-2)
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 is