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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.

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.

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)

Conduction is the main mode of heat transfer in solids. It occurs through the vibration of particles and the transfer of kinetic energy from one particle to another. Convection, on the other hand, involves the movement of fluid (liquid or gas) particles, and radiation is the transfer of heat through electromagnetic waves.

A DC motor works by a force exerted on a current-carrying coil in a magnetic field. To ensure the motor continues to rotate in one direction, the direction of the current in the coil must be reversed every half rotation. The commutator is a device that performs this function, reversing the current and ensuring that the torque always acts in the same direction, leading to continuous rotation.

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. $\therefore a=20ms^{-1}$

A bimetallic strip is made of two metals with different coefficients of linear expansion. When heated, the metal with the higher linear expansivity expands more than the other. This unequal expansion causes the strip to bend, with the more expansive metal on the outside of the curve. This principle is used in thermostats and thermometers

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.

Heat is a form of energy that is transferred from a hotter body to a colder body Temperature, on the other hand, is a measure of the average kinetic energy of the random motion of the molecules of a substance. The flow of heat is what causes a change in temperature.

The SI unit of electric current is the Ampere (A). It is a fundamental SI unit and is defined as one Coulomb of charge per second. A Volt is the unit of potential difference, an Ohm is the unit of resistance, and a Coulomb is the unit of electric charge.

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

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.

1. General wave equation: For a wave moving in the positive x-direction is y=Asin(kx−ωt), where A is amplitude, k is wave number, and ω is angular frequency.

2. Extract given values:

1. Amplitude (A) = 0.15 m
2. Frequency (f) = 550 Hz
3. Wavelength (λ) = 0.01 m

1. Calculate wave speed (v):
2. v=fλ=550 Hz×0.01 m=5.5 m/s

3. Calculate angular frequency (ω):

1. ω=2πf=2π×550=1100π rad/s

4. Calculate wave number (k):

1. k=$\frac{2π}{λ}=\frac{2π}{0.01}=200π rad/m$

5. Substitute values into the general equation:

1. y=0.15sin(200πx−1100πt)

6. Factor out 200π to match option A's format (y=Asin[k(x−vt)], where k=200π and v=5.5):

1. y=0.15sin[200π(x−(1100π/200π)t)]
2. y=0.15sin[200π(x−5.5t)]

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

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 relationship between wave velocity (V), frequency (f), and wavelength ($\lambda$ ) is given by the formula $V = f\lambda$ . To find the wavelength, we rearrange the formula to $\lambda = V/f$ . Substituting the given values, $\lambda = 340 m/s / 200 Hz = 1.7$ m.

Total Internal Reflection (TIR) is a phenomenon where a light ray is completely reflected back into the first medium. This occurs only under two specific conditions:

1. The light must travel from an optically denser medium (higher refractive index) to an optically rarer medium (lower refractive index).
2. The angle of incidence must be greater than the critical angle for that specific interface.

Isotopes of an element are atoms that have the same number of protons (atomic number) but a different number of neutrons. Because they have the same number of protons, they belong to the same chemical element. The difference in the number of neutrons results in different mass numbers. For example, Carbon-12 and Carbon-14 are isotopes of carbon, both having 6 protons, but Carbon-12 has 6 neutrons while Carbon-14 has 8 neutrons.

1. Given values:

1. Real Depth (Dreal​) = 6.0 m
2. Refractive Index (n) of water = 4/3

2. The formula for apparent depth: Apparent Depth (Dapp​) = Real Depth (Dreal​) / Refractive Index (n)

3. Substitute values and calculate:

1. Dapp​=$\frac{6.0m}{(\frac{4}{3})}$
2. Dapp​=$6.0*(\frac{3}{4})$
3. Dapp​= $\frac{18}{4}=4.5m$

A fuse is a safety device used in an electrical circuit to protect it from excessive current (overcurrent). It contains a wire designed to melt and break the circuit if the current flowing through it exceeds a certain rating, thus preventing damage to appliances or the risk of fire