24. A particle moving along the x-axis is acted upon by a single force F = F₀e⁻ᵏˣ, where F₀ and k are constants. The particle is released from rest at x = 0. It will attain a maximum kinetic energy of:
(A) F₀/k
(B)F₀/e^k
(C)kF_₀
(D)
(E) k^ekF₀

1. The current amplitude in an inductor in a radio receiver is to be 250 µÅ when the voltage amplitude is 3.60 V at a frequency of 1.60 MHz. What is the inductance?(A)13.4mH (B)2.78 mH (C) 10.8 mH (D) 1.43 mH (E) 4.01 mH

2. A conducting wire has a 1.0 mm diameter, a 2.0 m length, and a 50 mΩ resistance. What is the resistivity of the material?(A) 1.96×10⁻⁸Ω⋅m (B) 9.8×10⁻⁷Ω⋅m (C) 1.0×10⁻⁶Ω⋅m (D) 3.5×10⁻⁵Ω⋅m (E) 6.8×10⁻⁴Ω⋅m

3. A uniform rod of mass m and length L is freely pivoted at one end. What is the period of its oscillation? (I_system = 1/3 mL²)(A) 2π(L/g)¹/² (B) 2π(2L/3g)¹/² (C) 2π(L/3g)³/² (D) 2π(L/3g)¹/² (E) 2π(3L/g)¹/²

4. A hollow sphere of inner radius 8.0 cm and outer radius 9.0 cm floats half submerged in a liquid of specific gravity 0.80. Find the density of the material of which the sphere is made.(A) 2.1×10³ kg/m³ (B) 1.3×10³ kg/m³ (C) 1.5×10³ kg/m³ (D) 1.7×10³ kg/m³ (E) 1.9×10³ kg/m³

5. What will be the speed of a solid sphere of mass M and radius R₀ when it reaches the bottom of an incline if it starts from rest at a vertical height H and rolls without slipping? See Fig.5. Ignore losses due to dissipative forces. (A) (B) (C)(D) (E)

6. Each of four particles moves along an x-axis. Their coordinates (in meters) as functions of time (in seconds) are given byParticle 1: x(t) = 2.5 – 3.0t³Particle 2: x(t) = 2.5 + 3.0t³Particle 3: x(t) = 2.5 + 3.0t²Particle 4: x(t) = 2.5 – 1.5t – 3.0t²Which of these particles have (has) constant acceleration?(A) Only 1 and 2 (B) Only 2 and 3 (C) Only 1 and 3 (D) Only 3 and 4 (E) Only 4

7. The potential energy of a body of mass m is given by U(x) = -ax/(b²–x²), where a and b are constants. The corresponding force is:(A)(B) (C)(D)(E)

8. An infinite cylinder of radius R has a hole of radius a along its central axis. The rest of the cylinder has a uniform charge density ρ c/m⁻³. Determine the electric field in the region a ＜ r ＜ R.(A) (B)(C)(D) (E)

9. A small satellite is in elliptical orbit around Earth as shown in Fig.9. If L denotes the magnitude of its angular momentum and K denotes kinetic energy, then(A) L₂ ＞ L₁ and K₂ ＞ K₁ (B) L₂ ＞ L₁ and K₂ = K₁ (C) L₂ = L₁ and K₂ = K₁ (D) L₂ ＜ L₁ and K₂ = K₁ (E) L₂ = L₁ and K₂ ＞ K₁

10. A man launches a boat at a bridge and rows upstream a distance of 1 km where he drops a bottle in the water. He then continues to row upstream for an additional 10 min. At that point, he turns around and rows downstream, arriving at the bridge at the same time as the bottle. What is the speed of the water in the river? Assume that the man rows at the same speed relative to the water at all times.(A) 0.83 m/sec (B) 0.79 m/sec (C) 1.20 m/sec (D) 1.50 m/sec (E) 0.90 m/sec

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