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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

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.

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.

A vector quantity is a physical quantity that has both magnitude and direction. Momentum is a vector quantity, as it is the product of mass (a scalar) and velocity (a vector), and it has a direction. Speed, mass, and work are all scalar quantities, having only magnitude.

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 first equation of motion for uniformly accelerated motion is $v = u + at$ , where $v$ is the final velocity, $u$ is the initial velocity, $a$ is the acceleration, and $t$ is the time. We are given $u = 20$m/s, $a = 2$ m/s², and $t = 5$s. Substituting the values, we get $v = 20 + (2)(5) = 20 + 10 = 30$m/s.

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.

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 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.

Electrical power is transmitted over long distances using high-voltage transmission lines. The power loss in a transmission line is given by $P_{loss} = I^2R$ , where $I$ is the current and R is the resistance of the cable. The power being transmitted is $P = VI$ , where V is the voltage. For a constant power, if the voltage (V) is increased, the current (I) must be decreased. By decreasing the current, the power loss due to the heating effect of the current ($I^2R$ ) is significantly reduced, making the transmission more efficient

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

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

A galvanometer is a type of ammeter used to detect and measure very small electric currents. It is the core component of many analog measuring instruments, and it can be converted into an ammeter or a voltmeter by adding a shunt or a multiplier resistance, respectively

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

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

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.

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.

The key difference between a transverse wave and a longitudinal wave is the direction of vibration of the particles of the medium relative to the direction of wave propagation. In a transverse wave, the particles of the medium vibrate perpendicularly to the direction of wave propagation (e.g., light waves). In a longitudinal wave, the particles of the medium vibrate parallel to the direction of wave propagation (e.g., sound waves).

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

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)]