3.A small bead of mass m carrying a charge q is attached to one end of a massless string. The other end of the string is fixed to a uniformly charged vertical wall. Under the influence of both the gravity force and the electric force exerts on the bead (the gravitational acceleration is g), the string makes an angle θ = 30° to the wall when mechanical equilibrium of the system is achieved. What is the value of the surface charge density σ?

(A)
(B)
(C)
(D)
(E)

1.A mass block B of negligible size rests on a frictionless surface as shown in the right figure. An identical block A is attached to one end of a massless string of length L, and the other end of the string is located right above block B at height L. Block A is released from a height h = 0.5L and collides with B. The two blocks stick to each other and move together after the impact. How high will they rise above the surface? (A) h (B) 0.45h (C) 0.25h (D) 0.25L (E) 0.75L

2.Which quantity is conserved in the system of problem 1? (A) energy (B) momentum (C) angular momentum (D) mechanical energy (E) torque

4.The string-with-bead system in problem 3 will oscillate as a pendulum if it is perturbed from its equilibrium position. The length of the string is L. What is the period of this pendulum? (A) (B)(C) (D) (E)

5.When a spaceship circulates around a planet without using its power, why do the astronauts in it float? (A) Because there is no gravity in space. (B) Because there is air inside the spaceship. (C) Because the spaceship and the astronauts are free falling together. (D) Because the spaceship is too far from any massive body. (E) Because the spaceship can shield the astronauts from gravity.

6.Two infinite non-conducting sheets A and B having uniform surface charge densities 3σ and 4σ respectively intersect with each other at right angle. Find the magnitude of the electric field E between the sheets and the pressure p acting on sheet B due to sheet A. (A)(B)(C) (D)(E)

7.A rectangular conducting loop of width w = 10 cm and high h = 20cm rotates at 100 revolutions per second in a uniform magnetic field given by B = 100ŷ (mT) as shown in the right figure. What is the current induced in the loop if its resistance is 50Ω? (A) 251.2 mA (B) 251.2 sin(628t) mA (C) 251.2cos(628t) mA (D) 125.6 sin(628) mA (E) 502.4 mA

8.A cone of density ρ, height H and radius R floats in a liquid of density ρₒ as shown in the right figure. What is the ratio h/H of the exposed height to the total height? (A)(B)(C) (D)(E)

9.The vertical displacement of a wave propagating on a rope in x-direction can be written as y(x,t) = 2sin[(0.5x - 5t)π], where x and y are in centimeter, and t is in second. What is the velocity (in cm/s) of a particle on the rope at x = 1 cm, and t = 0.05 s? (A) 5√2π (B) 2√π (C) √2 (D) -√2/2π (E) 10

10.Two speakers radiate sound uniformly in all directions. The sound speed is 340 m/s. Both speakers are vibrating in phase at a frequency of 170 Hz and both have output power of      16xn      watt. A listener is standing at point C, which is 4 m away from speaker A and 2 m from speaker B. What is the intensity at C when both speakers are turned on?  (A) 0.75 W/m² (B) 1 W/m² (C) 0.25 W/m² (D) 2.25 W/m² (E) 1.25 W/m²

11.A container with cross section area A₁ has a hole at the bottom and is filled with water of height h. The area of the hole is A₂ (A₂ ＜＜ A₁) and the water starts to drain at t = 0. How long does it take to empty the container? (A)(B)(C)(D) (E)

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