37. A thin rod of length 100 cm and mass 6 kg with the rotation axis through its center. The rod rotates and accelerates to an angular velocity of 100 rad/s uniformly from rest over a 10 seconds interval. Find the torque to the rod (kg·m² /s² )?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25

33. A child uses a horizontal rope to pull a toy box weighing 100 N on a table. Given that the coefficient of kinetic friction between the box and the table is 0.05, what is the work done by the child to move the box 50 cm at a constant speed? (A) 0.25 J (B) 0.50 J (C) 2.5 J (D) 5.0 J (E) 10 J

34. A vertically hanging 16 kg block is connected to a cord wrapped around the rim of a flywheel with a diameter of 0.5 m. The flywheel's rotational inertia is 1.0 kg·m². Upon releasing the block and allowing the cord to unwind, what is the acceleration of the block? (Gravitational acceleration g = 10 m/s2 ) (A) 2 m/s2 (B) 3 m/s2 (C) 4 m/s2 (D) 5 m/s2 (E) 6 m/s2

35. A bullet weighing 100 g is diagonally fired into the end of a 0.5 m long stick with a speed of v0. The stick is suspended at point P. The rotational inertia of the stick relative to point P is 0.05 kg · m². When the bullet first enters the stick, the stick's angular velocity is 5.0 rad/s. What is the initial velocity of the bullet? (A) 7 m/s (B) 10 m/s (C) 15 m/s (D) 30 m/s (E) 40 m/s

36. A frictionless curve of radius 500 m is banked with a banking angle θ = 30°. A ball of mass m = 10 kg and radius r = 50 cm is moving on it. What angular velocity is needed for the ball moving on the curve without need of frictional force? (Gravitational acceleration g = 10 m/s2 ) (tan 30° = 0.577) (A) 53.7 rad/s (B) 107.4 rad/s (C) 214.8 rad/s (D) 332.2 rad/s (E) 429.6 rad/s

38. A gun fired vertically and hits a wooden block and stops inside. The bullet and block have a mass of 0.1 and 0.5 kg, respectively. The velocity of bullet is 100 m/s. How high will the wooden block be raised? (Gravitational acceleration g = 10 m/s2 ) (A) 8 m (B) 10 m (C) 12 m (D) 14 m (E) 16 m

39. One particle of mass M = 0.5 × 10-9 kg and velocity V = 4 × 105 m/s directly hits the other particle of mass m = 0.1 × 10-9 kg and velocity v = 0 m/s. Find the maximum energy transfer from one particle to the other? (A) 15 J (B) 22 J (C) 29 J (D) 36 J (E) 43 J

40. If two springs with spring constants k and 3k respectively are connected in series and attached to an object with mass m, what is the oscillation frequency of the springs? (A) (B) (C)(D) (E)

41. An electronics technician wishes to construct a parallel plate capacitor using rutile (κ = 100) as the dielectric. The area of the plates is 1.0 cm2 . What is the capacitance if the rutile thickness is 1.0 mm? (permeability constant μ0 = 8.85×10-12 C2 /N·m2 ) (A) 88.5 pF (B) 177 pF (C) 8.85 μF (D) 35.4 μF (E) 100 μF

42. Two conducting wires A and B of the same length and radius are connected across the same potential difference. Conductor A has twice the resistivity of conductor B. What is the ratio of the power delivered to A to the power delivered to B? (A) 2 (B) (C) 1 (D) (E)

43. A heart surgeon monitors the flow rate of blood through an artery using an electromagnetic flowmeter as shown in the figure. Electrodes A and B make contact with the outer surface of the blood vessel, which has a diameter of 3.0 mm. For a magnetic field magnitude of 0.04 T, an emf of 160 μV appears between the electrodes. Calculate the speed of the blood.(A) 1.33 m/s (B) 2.33 m/s (C) 3.66 m/s (D) 4.66 m/s (E) 6.66 m/s