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Myopia is a sight defect where the person can see near objects clearly but cannot focus on distant objects. The far point for a myopic person is closer than infinity. To correct this, a diverging (concave) lens is needed to form a virtual image of a distant object (at infinity) at the person's far point (2.0 m). Using the lens formula, $1/f = 1/u + 1/v$ , with $u = \infty$ and $v = -2.0$ m (virtual image at far point), we get $1/f = 1/\infty + 1/(-2.0) = 0 - 1/2 = -0.5$ . The focal length is $f = -2.0$ m. The power of the lens (P) is the reciprocal of the focal length in meters: $P = 1/f = 1/(-2.0) = -0.5$ D.

The principle of conservation of linear momentum states that in the absence of external forces, the total momentum of a system remains constant. A rocket uses this principle by expelling hot gases at high velocity in one direction. To conserve the total momentum of the rocket-gas system, the rocket itself gains momentum in the opposite direction, propelling it forward.

Most liquids expand when heated and contract when cooled. However, water behaves anomalously between 0°C and 4°C. When heated from 0°C to 4°C, water contracts and its density increases, reaching its maximum density at 4°C. When heated further above 4°C, it expands like a normal liquid

Resonance in a series R-L-C circuit occurs when the inductive reactance ($X_L$ ) is equal to the capacitive reactance ($X_C$ ). At this frequency, the circuit's impedance is at its minimum and is equal to the resistance (R), and the current is at its maximum.

Radiation is the transfer of heat through electromagnetic waves, and it does not require a material medium. The space between the Sun and the Earth is a vacuum, so heat can only be transferred by radiation. Conduction and convection require a medium for transfer

1. The deviation (δ) of a plane mirror is the angle between the incident ray's original path and the reflected ray's path. The formula δ=180∘−2i, where i is the angle of incidence (measured from the normal).

2. Identify given deviation: δ=120∘

3. Substitute into the formula and solve for i:

1. 120∘=180∘−2i
2. 2i=180∘−120∘
3. 2i=60∘
4. i=30∘

The energy stored in a capacitor (E) is given by the formula $E = \frac{1}{2}CV^2$ , where $ is the capacitance and $V$ is the potential difference. The capacitance of a parallel plate capacitor is given by $C = \frac{\epsilon A}{d}$ , which is constant if the area (A) and separation ($d$) are constant. If the potential difference (V) is doubled, the new potential difference is 2V. The new energy stored will be $E_{new} = \frac{1}{2}C(2V)^2 = \frac{1}{2}C(4V^2) = 4(\frac{1}{2}CV^2) = 4E$ . Therefore, the energy stored is quadrupled.

Surface tension is a property of a liquid that arises from the cohesive forces between the molecules at the surface of the liquid. These forces pull the surface molecules inward, causing the surface to behave like a stretched, elastic membrane. This effect minimizes the surface area of the liquid, which for a given volume, is a sphere

For resistors connected in parallel, the reciprocal of the total effective resistance ($R_T$) is the sum of the reciprocals of the individual resistances. The formula is $1/R_T = 1/R_1 + 1/R_2 + 1/R_3$ . Substituting the given values, we get $1/R_T = 1/2 + 1/3 + 1/6$ . Finding a common denominator, we get $1/R_T = 3/6 + 2/6 + 1/6 = 6/6 = 1$ . Therefore, $R_T = 1$ Ω.

In Simple Harmonic Motion, the acceleration of the oscillating body is directly proportional to its displacement from the equilibrium position and is always directed towards that position. Therefore, the acceleration is at its maximum at the extreme positions of the oscillation, where the displacement is at its maximum

The horizontal component of a force ($F_x$ ) is found by multiplying the magnitude of the force ($F$ ) by the cosine of the angle ($\theta$ ) it makes with the horizontal. The formula is $F_x = F \cos(\theta)$. Substituting the values, $F_x = 40 \cos(60^\circ) = 40 \times 0.5 = 20$ N.

In an enclosed space, such as a large hall or a stadium, sound waves can reflect off the walls, ceiling, and other surfaces. When these reflections arrive after the direct sound, they are called echoes. When the reflections are very rapid and merge with the original sound, it is called reverberation. Both of these phenomena interfere with the clarity of speech and music, making it difficult to understand what is being said.

When the stone is held at a certain height, it possesses gravitational potential energy. As it is dropped, this potential energy is converted into kinetic energy, the energy of motion. The potential energy is at its maximum at the beginning of the fall and becomes zero at the ground, while the kinetic energy is zero at the beginning and becomes maximum just before it hits the ground

The critical angle is the angle of incidence in the denser medium for which the angle of refraction in the less dense medium is 90°. When the angle of incidence exceeds the critical angle, the light ray is no longer refracted, but is instead totally internally reflected into the denser medium.

This is a calorimetry problem based on the principle of heat exchange: Heat lost by hot object = Heat gained by cold objects (water and calorimeter).

1. Given values:

1. Mass of metal (mm​) = 0.5 kg
2. Initial temp of metal (Tm,i​) = 100°C
3. Final mixture temp (Tf​) = 25°C
4. Initial temp of water/calorimeter (Tw,i​,Tcal,i​) = 15°C
5. Heat capacity of water (Cw​) = $420 J K^{-1}$ (This is the total heat capacity, not specific)
6. Heat capacity of calorimeter (Ccal​) = $80 J K^{-1}$ (Total heat capacity)

2. Calculate temperature changes:

1. Temperature change of metal (ΔTm​) = Tm,i​−Tf​=100∘C−25∘C=75∘C=75 K
2. Temperature change of water (ΔTw​) = Tf​−Tw,i​=25∘C−15∘C=10∘C=10 K
3. Temperature change of calorimeter (ΔTcal​) = Tf​−Tcal,i​=25∘C−15∘C=10∘C=10 K

3. Apply heat exchange equation:

1. Heat Lost by Metal = (Heat Gained by Water) + (Heat Gained by Calorimeter)
2. mm​cm​ΔTm​=Cw​ΔTw​+Ccal​ΔTcal​

4. Substitute values and solve for cm​ (specific heat capacity of the metal):

1. 0.5×cm​×75=(420×10)+(80×10)
2. 37.5cm​=4200+800
3. 37.5cm​=5000
4. cm​=$\frac{5000}{37.5}≈133.33 J kg^{-1} K^{-1}$

Rectification is the process of converting alternating current (AC), which periodically reverses direction, into direct current (DC), which flows only in one direction. This is typically done using semiconductor diodes, which allow current to flow in one direction only

The half-life is the time it takes for half of the radioactive atoms in a sample to decay. In 30 years, there will have been 3 half-lives (30 years / 10 years/half-life = 3 half-lives). After the first half-life, 1/2 of the sample remains. After the second, 1/2 of that remains, which is 1/4 of the original. After the third half-life, 1/2 of the 1/4 remains, which is 1/8 of the original sample

1. Identify the velocity equation: v=10+2t2

2. Recall relationship between velocity and acceleration: Acceleration (a) is the first derivative of velocity with respect to time ( $a=\frac{dv}{dt}$ )

3. Differentiate the velocity equation:

1. $a=\frac{d}{dt}(10+2t^2)$
2. a=0+2×2t
3. a=4t

4. Substitute the given time (t=5 s):

1. $a=4×5=20 ms^{-1}$
2. $\therefore a=20ms^{-1}$

1. Identify given values:

1. Mass (m) = 500g = 0.5 kg
2. Extension (x) = 20cm = 0.2 m
3. Final velocity (v) = 40 m/s

2. Apply Work-Energy Theorem: The work done by the catapult equals the change in kinetic energy of the stone.

1. Work Done (W) = Force (F) × Distance (x)
2. Kinetic Energy (KE) = $\frac{1}{2}mv^2$
3. Therefore, $F*X=\frac{1}{2}mv^2$

3. Substitute values and solve for F:

1. $F*0.2=\frac{1}{2}*0.5*40^2$
2. F×0.2=0.25×1600
3. F×0.2=400
4. $F=\frac{400}{0.2}=2000 N$
5. $\therefore$ F=2.0×10³ N

The electric potential difference (or voltage) between two points is defined as the work done per unit positive charge in moving the charge from one point to the other. It is measured in Volts (V), which is equivalent to Joules per Coulomb (J/C)