Physics

Capacitive reactance (Xc) is calculated using the formula Xc = 1 / (2πfC). Given f = 50 Hz and C = 100 µF = 100 × 10⁻⁶ F, substituting these values gives Xc = 1 / (2 × 3.1416 × 50 × 100 × 10⁻⁶) ≈ 31.83 Ω. The closest option to this value is 32 Ω, which corresponds to option A. Therefore, the correct answer is A (32 Ω).

An alpha particle ionizes an atom primarily through direct collision with the atom's electrons, knocking them out and creating ions. Electrostatic forces (attraction or repulsion) influence the interaction but ionization occurs mainly due to the direct impact.

A body in equilibrium experiences no net force, so it can either be at rest or move with uniform velocity (constant speed in a straight line). Hence, it may be at rest or in uniform motion.

The maximum safe radiation dose limit for persons working in a nuclear power station is generally set at 5 rem (50 millisieverts) per year, not per week. This corresponds to about 0.1 rem per week on average. The options given in the question are weekly dose limits, which are not standard. However, among the options, 5 rem per week (option B) is the only one that matches the internationally recognized annual dose limit of 5 rem (50 millisieverts) when considered over a year (5 rem/week × 52 weeks = 260 rem/year, which is much higher than the annual limit, so the weekly framing is misleading). The standard regulatory limit is 5 rem per year, so none of the weekly values are strictly correct. But since the question asks for a weekly limit, 5 rem per week is the closest to the correct annual limit. Therefore, the correct answer is B.

Mass defect per nucleon is defined as the packing fraction, which represents the mass defect divided by the total number of nucleons. It is a measure of the average mass defect per nucleon in a nucleus.

Alpha particles consist of two protons and two neutrons, giving them a net positive charge of plus two. Therefore, the correct answer is 'Plus two'.

TV sets primarily emit very low-level non-ionizing electromagnetic radiation, mainly in the radio-frequency range, with older cathode-ray tube (CRT) TVs capable of emitting very low levels of X-rays, but these are limited to background levels and are not harmful. Microwave ovens emit non-ionizing microwave radiation at about 2.45 GHz, which is far lower in energy than gamma rays. They are designed with safety features to prevent microwave leakage beyond strict regulatory limits. Therefore, TV sets and microwave ovens do not emit gamma rays (γ-rays), but rather non-ionizing radiation, with TV sets potentially emitting very low-level X-rays in older models. Among the options given, X-rays (A) is the closest correct answer for TV sets, while microwave ovens emit microwaves, which are not listed as an option. The original answer (D) gamma rays is incorrect.

The mass of a neutron is approximately 1.67 x 10^-27 kilograms, which is close to the mass of a proton and much larger than the mass of an electron.

A meter rod generally has a least count of 1 mm (0.001 m), so measurements should not be recorded beyond three decimal places in meters. Record (i) is too precise, while (iii) implies an accuracy not possible with a standard meter rod. Therefore, 0.21 m is the most appropriate recorded value.

X-rays and gamma rays (γ-rays) are both types of electromagnetic waves, differing mainly in their origin and energy. Therefore, X-rays are electromagnetic waves like γ-rays.

Gamma rays (γ-rays) have high penetration power, allowing them to reach infections inside the body effectively, unlike alpha or beta rays which have low penetration. X-rays also penetrate but are less commonly used for treating infections compared to gamma rays in medical therapies.

A linear accelerator is a device specifically designed to accelerate charged particles, such as nuclei, to high velocities using electromagnetic fields. The other options are detection or measurement devices, not accelerators.

A body is in complete equilibrium only when both the first condition (the net force is zero) and the second condition (the net torque is zero) are satisfied simultaneously. This ensures the body is neither translating nor rotating.

Cobalt-60 is commonly used in radiotherapy to treat various types of cancer due to its gamma radiation, which can target and destroy cancer cells effectively. The other isotopes listed are not typically used for cancer treatment.

The International System of Units (SI) primarily consists of two types of units: base units and derived units. Base units are fundamental, while derived units are combinations of base units.

The magnitude of the cross product of two vectors A and B is |A||B|sinθ, and the dot product is |A||B|cosθ, where θ is the angle between the vectors. Setting these equal gives |A||B|sinθ = |A||B|cosθ, which simplifies to sinθ = cosθ. This equality holds true at θ = 45° (π/4 radians) and θ = 135° (3π/4 radians). Since the angle between vectors is typically taken as the smaller angle, the principal solution is θ = 45°. Therefore, the angle between the two vectors when the magnitude of the cross product equals the dot product is 45°, corresponding to option B.

J.J. Thomson's atomic model, also known as the 'plum pudding model,' proposed that the atom is a uniform sphere of positive charge with electrons embedded within it, implying uniform density. Rutherford's and Bohr's models do not assume uniform density of the atom.

Pair production requires the presence of a heavy nucleus to conserve momentum, while energy and charge conservation are fundamental principles always upheld. Thus, net energy, net charge, and net momentum are all conserved during the process, making option D correct.

Measurement errors can arise from multiple sources including human inexperience, faulty equipment or apprentices, and inappropriate methods. Therefore, all the reasons listed in options A, B, and C can cause errors in measurement.

A zero in a measurement may or may not be significant depending on its position and context. For example, zeros between significant digits are significant, while leading zeros are not. Therefore, zeros can be significant or insignificant.

Pair production requires photons with energy greater than 1.022 MeV, which is typically found in gamma rays. X-rays generally do not have sufficient energy, and UV or IR rays have even lower energies, making gamma rays the correct choice.

Uncertainty in measurement can arise from multiple sources including the limitations of the measuring instrument, natural variations in the object being measured, and inadequate measurement techniques. Therefore, all options A, B, and C contribute to measurement uncertainty.

Cadmium rods are used in nuclear reactors as control rods because cadmium has a high neutron absorption cross-section, which helps control the fission chain reaction by absorbing excess neutrons.

Alpha particles are positively charged and relatively heavy, so when they move in a uniform electric or magnetic field, their path is generally straight (rectilinear) unless acted upon by external forces. They do not move in zig-zag or erratic paths under normal conditions.

Options B and C both represent the same vector with components (1/√3) along each axis, which has a magnitude of 1, making it a unit vector. Option A has components √3, which results in a magnitude greater than 1, so it is not a unit vector.