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Specific gravity (SG) is the ratio of the density of the liquid (\(\rho_l\)) to the density of water (\(\rho_w\)): \( \mathrm{SG} = \frac{\rho_l}{\rho_w} \) Rearranging for density: \((\rho_l = \mathrm{SG} \times \rho_w = 0.76 \times 1000 = 760 \, \mathrm{kg \, m^{-3}}\)

\(C = \frac{Q}{\Delta T} = \frac{48000 \, \text{J}}{53 \, \text{ºC}} \approx 905.66 \, \text{J/ºC}\)

\(F = m \cdot g = 1.5 \, \text{kg} \times 10 \, \text{m/s}^2 = 15 \, \text{N}\) \(A = \pi r^2 = \pi (0.003 \, \text{m})^2 = \pi (9 \times 10^{-6}) \approx 2.827 \times 10^{-5} \, \text{m}^2\) \(\text{Stress} = \frac{F}{A} = \frac{15 \, \text{N}}{2.827 \times 10^{-5} \, \text{m}^2} \approx 5.299 \times 10^5 \, \text{Pa}\)

The apparent depth of an object in water (as viewed from air) is less than the real depth due to refraction. The relationship is given by: \(\mu = \frac{\text{Real depth}}{\text{Apparent depth}}\) where \(\mu\) is the refractive index of water (\(\mu = 1.33\)). Rearranging for real depth: \(\text{Real depth} = \mu \times \text{Apparent depth} = 1.33 \times 10 \, \text{cm} = 13.3 \, \text{cm}\)

\(B = \frac{F}{q \cdot v \cdot \sin \theta}\) \(\theta = 45^\circ \implies \sin 45^\circ = \frac{\sqrt{2}}{2}\) Substituting the values: \(B = \frac{6}{(5 \times 10^{-6})(3 \times 10^4) \left(\frac{\sqrt{2}}{2}\right)}\) Simplifying: \(B = \frac{6}{(15 \times 10^{-2}) \left(\frac{\sqrt{2}}{2}\right)} \approx \frac{6}{0.1061} \approx 56.5 \, \text{T}\)

Photovoltaic cells use semiconductor materials, such as silicon, to convert sunlight into electricity through the photovoltaic effect.

D. 2666.7 \(\text{J kg}^{-1} \, \text{K}^{-1}\) Using the formula: \(Q = mc\Delta T\) We can rearrange to find \( c \): \(c = \frac{Q}{m \Delta T} = \frac{1000}{0.025 \times 15} = \frac{1000}{0.375} = 2666.7\) Thus, the specific heat capacity is: \(c = 2666.7 \, \text{J kg}^{-1} \, \text{K}^{-1}\).

B. \( 6.1 \times 10^{-31} \, \text{kg} \) Using the de Broglie wavelength: \(\lambda = \frac{h}{p}\) Rearranging gives: \(p = \frac{h}{\lambda}\) Given: \(\lambda = 4.0 \times 10^{-7} \, \text{mm} = 4.0 \times 10^{-10} \, \text{m}\) Now substituting for \( p \): \(p = \frac{6.63 \times 10^{-34}}{4.0 \times 10^{-10}} = 1.6575 \times 10^{-24} \, \text{kg m/s}\) Now, to find mass \( m \): \(m = \frac{p}{v} = \frac{1.6575 \times 10^{-24}}{2.7 \times 10^{8}} \approx 6.1 \times 10^{-31} \, \text{kg}\).

E = \(\frac{\text{Kq}}{r^2}\) r = \(\sqrt{\frac{\text{Kq}}{\text{E}}}\) r = \(\sqrt{\frac{9.0 \times 10^9 \times 1.2 \times 10^{-7}}{4.8 \times 10^{-4}}}\) r = \(\sqrt{2.25 \times 10^6}\) = 1500m = 1.5km

\(\gamma\) = 3 \(\alpha\) \(\gamma\) = 3 x 24 x 10\(^{-6}\) = 72 x 10\(^{-6}\)k\(^{-1}\) V\(_2\) = V\(_1\)(1 + \(\gamma\) ∆T) V\(_2\) = 3.48 x (1 + 72 x 10\(^{-6}\)k\(^{-1}\) x 306) V\(_2\) = 3.48 x (1 + 0.022032) V\(_2\) ≈ 3.56cm\(^3\)

Induced emf (electromotive force) refers to the voltage generated across a conductor or circuit due to a changing magnetic field, as explained by Faraday's laws of induction. This voltage drives the flow of induced current when the circuit is complete.

The ampere is a fundamental SI base unit, representing electric current, and is one of the seven base units used in physics

A. Reduce the friction of fluid. The pointed front of a boat or airplane is designed to minimize drag and reduce the frictional resistance as it moves through water or air, enhancing efficiency and improving performance.

Equivalent \(\, emf \, E_{eq} = 1.5 \, \text{V} \, (\text{same as single cell})\). Equivalent \(\, internal \, resistance \, r_{eq} = \frac{1}{2} = 0.5 \, \Omega \, (\text{parallel})\). Total \(\, resistance \, R_{total} = r_{eq} + 2 = 2.5 \, \Omega\). Current \(\, I = \frac{E_{eq}}{R_{total}} = \frac{1.5}{2.5} = 0.6 \, \text{A}\).

LASER stands for Light Amplification by Stimulated Emission of Radiation. It works when an incoming photon makes an excited electron release another identical photon, producing a coherent, highly focused beam of light.