Physics

Materials that undergo plastic deformation before breaking are called ductile materials because they can deform significantly without fracturing. Brittle materials break without noticeable deformation, amorphous refers to non-crystalline structure, and polymers are a class of materials that can be ductile or brittle.

Diffraction fringes produced by a single slit or double slit are generally equally spaced due to the consistent path difference between adjacent maxima or minima. Therefore, the distance between fringes remains constant, making option A correct.

The appearance of color in thin films is due to interference of light waves reflected from the different surfaces of the film, causing constructive and destructive interference at different wavelengths.

Gravitational potential energy (P.E.) of a body is given by the formula mgh, where m is mass, g is acceleration due to gravity, and h is height. Therefore, it has a specific formula.

The central spot of Newton's rings is dark because there is a path difference of half a wavelength due to the air film between the lens and the glass plate, causing destructive interference at the center.

The slope of a work versus time graph represents the rate of change of work with respect to time, which is power. Power is defined as the work done per unit time (P = ΔW/Δt) and is measured in watts (joules per second). Therefore, the slope of a work vs time graph corresponds to power, not displacement, acceleration, or energy. Option C (power) is the correct answer.

Geothermal energy is derived from the natural heat of the Earth, which is continuously produced and thus considered a renewable source of energy. It is sustainable and does not deplete over time like fossil fuels.

The dot product of force and velocity gives power, which is the rate at which work is done. This is because power = force · velocity (dot product).

Work done by a force is given by W = Fd cosθ, where θ is the angle between force and displacement. The work is maximum when cosθ = 1, which occurs at θ = 0°, meaning force and displacement are in the same direction.

The energy stored per unit volume (strain energy density) in an elastic material is given by (1/2) × Young's modulus × (strain)^2, which corresponds to (Y∝²)/2. This matches option C.