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Given: u = -6 cm (the object is 6 cm from the eye, and the direction is negative), v = 10 cm (the image is 10 cm from the eye) Using the lens formula: \(\frac{1}{\text{f}}\) = \(\frac{1}{\text{v}}\) - \(\frac{1}{\text{u}}\) \(\frac{1}{\text{f}}\) = \(\frac{1}{10}\) + \(\frac{1}{6}\) \(\frac{1}{\text{f}}\) = \(\frac{8}{\text{30}}\) So that f = 3.75cm upon cross multiplying Therefore, the focal length of the lens is 3.75 cm.

When white light passes through a prism, dispersion occurs because different colors (wavelengths) of light travel at different speeds in the glass. This causes the colors to spread out and form a spectrum, with red bending the least and violet bending the most.

The speed of sound depends on the density of the medium in which it travels and increases when the density increases. For example, in solids sound travels faster than in liquid and even faster than in gas, and the density is highest in solids, lower in liquids, and lowest in gas. Hence, sound travels fastest in solids.

\(v = f\lambda\) \(v = 2f \times (l_{2} - l_{1})\) \(v = 2 \times 600 \times(0.413 - 0.130)\) \(v = 1200 \times 0.283\) \(v = 339.6ms^{-1}\)

As the vibrating tuning fork is brought closer to the end of the pipe, it causes the air column in the pipe to resonate. This resonance amplifies the sound waves, leading to an increase in loudness. The air column vibrates at specific frequencies, enhancing the sound produced by the tuning fork.

Harmonics are additional frequencies that accompany the fundamental frequency of a sound. Each instrument produces a unique harmonic spectrum, giving it a distinct timbre. This allows the ear to distinguish between notes played on different instruments, even at the same pitch. Pitch refers to the frequency of the sound. Speed is not a relevant factor in distinguishing instruments . Loudness relates to the intensity of sound, not its quality

A capacitor can be used in circuits with induction coils to smooth out voltage spikes and reduce arcing at the contacts. It helps absorb sudden changes in voltage, thereby minimizing wear and prolonging the life of the contacts.

The energy(W)stored in an inductor is calculated by the formula: \(\frac{1}{2}\)LI\(^2\) = \(\frac{1}{2}\) x 10 x (0.2)\(^2\) = 0.2J

The inductive reactance (X\(_L\)​) of an inductor is given by the formula: Given: X\(_L\) = 1\(\Omega\), f = 50Hz X\(_L\) = 2\pifL L = \(\frac{1}{2\pif}\) = \(\frac{1}{2\pi \times50}\) = \(\frac{1}{100\pi}\) = 3.183 x 10\(^{-3}\)H

Bohr's theory of the atom introduced the concept of quantized energy levels for electrons in an atom. It explained how electrons occupy specific energy levels and how they can jump between these levels by absorbing or emitting energy in the form of photons.

The acceleration due to gravity (g) is affected by the distance from the center of the Earth, the latitude, and the rotation of the Earth. However, the mass of the object does not affect g; all objects fall at the same rate in a vacuum, regardless of their mass.

Making the area large and the separation small will increase the capacitance.

\(\frac{1}{\text{R}}\) = \(\frac{1}{2}\) + \(\frac{1}{3}\) = \(\frac{5}{6}\) R = \(\frac{6}{5}\) = 1.2\(\Omega\); So p.d through the 3\(\Omega\) and 2\(\Omega\) resistors in parallel = 1.5 x 1.2 =1.8V So the current through the 3\(\Omega\) resistor(I) = \(\frac{\text{V}}{\text{R}}\) = \(\frac{1.8}{3}\) = 0.6A (recall V = IR)

Given: P = 120W, t = ?, m of water = 1.2kg, c of water = 4200Jkg\(^{-1}\)K\(^{-1}\), \DeltaT = 15ºC Q = pt = m c \DeltaT 120 x t = 1.2 x 4200 x 15 = 75600J t = \(\frac{75600}{120}\) = 630secs → 10.50minutes.

"magnetic field" is the term that describes the region where magnetic effects are felt.