Physics

When a force acts parallel to the direction of motion, the work done is maximized because work is calculated as the product of force, displacement, and the cosine of the angle between them. Here, the angle is zero degrees, so cosine is 1, giving maximum work.

The energy stored in a stretched wire is equal to the work done to stretch it, which is given by the formula: Energy = (1/2) × Force × Extension. Here, the force is 20 N and the extension is 1 mm (0.001 m). Therefore, the energy stored = 0.5 × 20 × 0.001 = 0.01 J. This matches option A. The original explanation correctly calculated the energy but the correct answer was incorrectly marked as B. The correct answer is A.

In intrinsic semiconductors, increasing temperature excites more electrons from the valence band to the conduction band, thereby increasing the number of charge carriers and thus increasing electrical conductivity.

The energy required to magnetize and demagnetize a material is represented by the area of the hysteresis loop. This area corresponds to the energy loss per cycle due to magnetic hysteresis.

The modulus of elasticity (also known as Young's modulus) is defined as stress divided by strain. Stress has units of force per unit area (N/m²), and strain is dimensionless, so the modulus of elasticity has units of N/m², which is equivalent to Pascal (Pa).

According to the band theory of solids, semiconductors have a completely filled valence band and a totally empty conduction band at absolute zero temperature, separated by a narrow forbidden energy gap (band gap). This band gap is small enough to allow thermal excitation of electrons from the valence band to the conduction band at room temperature, enabling electrical conductivity. Option B correctly describes this: a completely filled valence band, a totally empty conduction band, and a narrow forbidden band. Option A is incorrect because it states a partly filled valence band, which is not true for semiconductors. The valence band is fully occupied at 0 K. Option C incorrectly states a partially filled conduction band, which is not typical for intrinsic semiconductors. Option D incorrectly states a partly filled valence band and a wide forbidden band, which does not describe semiconductors.

The slit spacing (d) of a diffraction grating is the reciprocal of the number of lines per unit length. Given 500 lines per mm, the slit spacing d = 1/500 mm = 0.002 mm = 2 x 10^-3 mm. This matches option D. The original answer C (2 x 10^-5 mm) is incorrect. The explanation is that the slit spacing is the inverse of the number of lines per mm, so for 500 lines/mm, d = 1/500 mm = 0.002 mm = 2 x 10^-3 mm.

Crystals have a regular, repeating atomic structure that can diffract X-rays or other waves, acting like a diffraction grating. This property is fundamental in crystallography for analyzing crystal structures.

The energy stored in a stretched wire within the elastic limit is the elastic potential energy given by (1/2) × force × extension. Using Hooke's law, the force F is proportional to the extension E with spring constant k = EA/L, where A is the cross-sectional area and L is the original length. The energy stored is therefore (1/2)kE² = (1/2)(FE/L)E = FE²/(2L). Among the given options, FE²/L (option C) is the closest and dimensionally consistent expression representing the energy stored (ignoring the factor 1/2). Hence, option C is correct.

Work done on a body results in a change in its total mechanical energy, which includes both kinetic energy (K.E.) and potential energy (P.E.). Therefore, the work done equals the change in K.E. plus the change in P.E.

A vacant or partially filled band in a solid is called the conduction band because it contains electrons that are free to move and conduct electricity. The valence band is typically fully filled, the forbidden band refers to the energy gap, and 'empty band' is not a standard term.

The strain energy per unit volume (also called strain energy density) stored in an elastic material under stress without exceeding the elastic limit is given by (1/2) × stress × strain. Among the given options, 'Stress x strain' (option C) is the closest to the correct formula, although it ideally should include the factor 1/2. The other options are incorrect as they do not represent the energy per unit volume.

One megawatt hour (MWh) is equal to 1,000,000 watts multiplied by 3600 seconds, which equals 3.6 x 10^9 joules. This is confirmed by multiple authoritative sources. Therefore, the correct answer is option C: 36 x 10^9 J (which is equivalent to 3.6 x 10^10 J, but the intended meaning is 3.6 x 10^9 J). The originally marked answer A (36 x 10^6 J) is incorrect as it equals 3.6 x 10^7 J, which is much smaller than the actual value.

A ferromagnet becomes fully magnetized when subjected to a direct current (D.C.) at its peak value, as this provides a steady magnetic field that aligns the magnetic domains. Alternating current (A.C.) continuously changes direction, preventing full magnetization.

When two protons are brought closer, the electrostatic repulsive potential energy between them increases because like charges repel each other, raising their potential energy.

Holes, which are the absence of electrons acting as positive charge carriers, can exist in conductors, insulators, and semiconductors. However, they are most significant and commonly discussed in semiconductors. Since holes can theoretically exist in all these materials, the correct answer is 'All of the above'.

Momentum is directly proportional to velocity, so doubling velocity doubles momentum. Kinetic energy is proportional to the square of velocity, so doubling velocity increases kinetic energy by four times.

An object that emits its own light is called luminous. Non-luminous objects do not produce their own light, incandescent refers to emitting light due to heat, and bright describes the intensity of light, not the source.

In the double slit experiment, covering one slit removes the possibility of interference between two coherent sources, so no interference fringes are observed. However, diffraction from the single open slit still occurs, so diffraction fringes can be seen.

A blue book appears blue because it reflects blue light. Under monochromatic red light, there is no blue light to reflect, so the book absorbs the red light and appears black.

Einstein proposed that light travels as discrete packets of energy called photons, which explained the photoelectric effect. This concept established the particle nature of light alongside its wave properties.

Isotropy refers to the property of being identical in all directions, meaning the density of atoms remains the same along any direction in a crystal. Homogeneity means uniform composition throughout but does not specifically imply directional uniformity.

Stress is defined as force per unit area. Force has dimensions MLT⁻² and area has dimensions L², so stress dimensions are MLT⁻² divided by L², which simplifies to ML⁻¹T⁻².

Stress, Young's modulus, and pressure all have the dimensions of force per unit area (N/m² or Pascal). Strain, however, is a dimensionless quantity representing deformation relative to original length, so it does not have dimensions of force per unit area.

Jupiter has the highest escape velocity among the planets in the solar system due to its large mass and size, which creates a stronger gravitational pull compared to other planets.