Answer all 20 questions or as many as you can.
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Q.1. A block of mass M, at rest on a horizontal, frictionless table, is attached to a rigid support by a spring of force constant k. A bullet of mass m and speed v strikes the block as shown below. The bullet remains embedded in the block. The amplitude of the resulting harmonic motion is,
Q.2 Consider the Hamiltonian of a system of mass m,
For this system,
a) x and y components of momentum are constants of motion
b) z component of momentum is a constant of motion
c) x component of momentum is a constant of motion
d) y component of momentum is a constant of motion
e) none of the above

Q.3 For a conservative force F, which one of the following is true
d) None of the above
e) a, b and c are all true

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Q.4 A man stands on a frictionless platform that is rotating with an angular speed of 1.22 rev/s; his arms are outstretched and he holds a weight in each hand. With his hands in this position the total rotational inertia of the man, the weights, and the platform is 6.13 kg.m2. If by moving the weights the man decreases the rotational inertia to 1.97 kg.m2, the resulting angular speed is
a) 3.8 rev/sec
b) 1.9 rev/sec
c) 7.6 rev/sec
d) 1.1 rev/sec
e) 9.8 rev/sec

Q.5 A car of mass m starts at rest and is driven with constant power. After it covers a
distance x, the speed v is,

Q.6 A sphere of radius R carries a non-uniform charge distribution rρα=, where αis a constant and r is the distance from the center of the sphere. The electric field E inside the sphere is proportional to,

Q.7 Use Gauss' law to determine the electric field between two coaxial cylinders of infinite length and of radii a and b>a. If the inner one has a total charge per unit length of -Q L while the outer cylinder has a charge per unit length Q L the capacitance is proportional to,

Q.8 Two point charges are located on the x-axis. The first is e−at x=0 and the second is + e at x = a. The potential energy in this system of charges is proportional to,