Physics

The valence electrons occupy the valence band, which is the highest range of electron energies where electrons are normally present at absolute zero temperature. The conduction band is above the valence band and is typically unoccupied unless electrons gain enough energy.

An n-type semiconductor is doped with donor atoms that add extra electrons, which are negatively charged. However, the material as a whole remains electrically neutral because the number of positive charges (protons in the lattice) balances the number of negative charges (electrons). Thus, the net charge on n-type material is neutral.

When a wire is stretched within its elastic limit, it behaves like a spring obeying Hooke’s law. The work done (and hence elastic potential energy stored) is equal to the area under the force-extension graph, which is (1/2)Fx.

Work and torque both have the same dimensional formula, which is M L^2 T^-2. This is because work is force times distance and torque is force times lever arm distance, so their dimensions match.

The band theory of solids explains the electronic properties of all types of materials: electrical insulators, conductors, and semiconductors. It describes how the energy bands and band gaps determine whether a material conducts electricity or not, thus satisfactorily explaining all these categories.

When the arrow is released, the elastic potential energy stored in the stretched bow is converted into the kinetic energy of the moving arrow.

Coercive force is the magnetic field strength required to reduce the magnetization of a material to zero after it has been magnetized; thus, it opposes demagnetization.

Deformation refers to any change in shape, length, or volume of a body when subjected to an external force, which matches the definition given in the question.

Young's modulus (also called the modulus of elasticity) is defined as the ratio of stress to strain within the elastic limit of a material under tension or compression. Stress is the force per unit area applied, and strain is the relative change in length (extension/original length). Young's modulus is a constant for a given material in the elastic region, representing how stiff the material is. It is not proportional to strain; rather, it is the constant ratio stress/strain. Therefore, the correct interpretation is that Young's modulus is the ratio of stress to strain, making option B correct.

A conservative field is defined as a field in which the work done in moving a body along any closed path is zero. This is a fundamental property distinguishing conservative fields from non-conservative ones.

Tidal energy is generated primarily due to the gravitational pull of the Moon on Earth's oceans, causing tides. While the Sun also influences tides, the Moon's effect is dominant, making it the main source of tidal energy.

Photovoltaic cells convert solar energy directly into electrical energy by the photovoltaic effect, making option B correct. Rotary and galvanic cells do not perform this function, and 'non of these' is incorrect.

Young's modulus is calculated using the formula Y = (F/A) / (ΔL/L). Given F = 10 N, A = 2 cm² = 2×10⁻⁴ m², L = 1 m, and ΔL = 0.01 m, substituting these values yields Y = (10 / 2×10⁻⁴) / (0.01 / 1) = 5×10⁶ N/m², which corresponds to option B.

Steel has the highest elasticity among the given substances because it has a high Young's modulus, meaning it can undergo significant stress with minimal strain before deforming permanently. Rubber, glass, and copper have lower elastic moduli compared to steel.

Work done by a variable force is determined by dividing both the force and displacement into small intervals and summing the product of force and displacement over these intervals, effectively calculating the integral of force over displacement.

One horsepower (hp) is defined as exactly 746 watts (W). This is a standard conversion used in physics and engineering to relate mechanical power to electrical power.

The work done by the force of friction is always negative because friction opposes the direction of motion, removing energy from the system.

The diffraction experiment demonstrates that light waves have much smaller wavelengths than sound waves because light diffracts less noticeably than sound under similar conditions. This difference in diffraction patterns indicates the smaller wavelength of light compared to sound.

The energy stored in the wire is given by (1/2) × stress × strain × volume. Using Young's modulus (Y = stress/strain), the energy stored can be calculated as (1/2) × Y × (strain)^2 × volume. Substituting the given values yields approximately 0.025 J, which corresponds to option A.

Electrons in the conduction band are free to move and thus can transport electric charge, which is the fundamental principle behind electrical conductivity in materials.

Momentum is directly proportional to velocity, so doubling the speed doubles the momentum. Kinetic energy depends on the square of the speed, so it actually quadruples, not doubles. Potential energy depends on height, not speed, and acceleration is unrelated to speed in this context.

The bright central portion in the shadow of a ball is due to diffraction, where waves bend around the edges and interfere constructively at the center, creating a bright spot known as the Poisson or Arago spot.

The escape velocity from the Earth's surface is approximately 11.2 km/s. Among the given options, 9.5 km/s (option C) is the closest to the true value. The originally marked answer 'B' (7.5 km/s) is incorrect. The escape velocity is calculated by the formula v = sqrt(2GM/r), and for Earth, it is about 11.2 km/s.

Tides typically cause the sea level to rise and fall about twice each day due to the gravitational pull of the moon and the sun, resulting in two high tides and two low tides approximately every 24 hours.

The escape velocity (V_esc) is related to the orbital velocity (V_o) by the formula V_esc = √2 × V_o, which is approximately 1.414 times V_o. This means the escape velocity is about 1.414 times the orbital speed at the same distance from the central body. Among the given options, the closest correct relation is V_esc = 2 V_o, which is option D. Although the exact factor is √2 (approximately 1.414), option D is the best available choice in the given options.