This is known as the Parallel Axis Theorem, which states that I = Σ(m_i * r_i^2).

The moment of inertia is calculated by summing the products of mass and the square of the distance from the axis of rotation.

The total moment of inertia for a system of particles is the sum of each particle's moment of inertia, I_total = Σ(m_i * r_i^2).

The total moment of inertia for a system of particles is calculated by adding the individual moments of inertia.

The moment of inertia of a thin circular ring about an axis through its center and perpendicular to its plane is I = MR^2.

The magnetic field inside a toroid is given by B = μ₀NI/2πR.

For r > R, the electric field behaves as if all the charge were concentrated at the center, given by E = Q/(4πε₀r²).

In a zero-order reaction, the concentration of reactants decreases linearly with time.

In a zero-order reaction, the rate is constant and does not depend on the concentration of reactants.

In a zero-order reaction, the rate is constant and does not depend on the concentration of the reactants.

For a zero-order reaction, t = [A₀ - A] / k. Here, t = (0.5 - 0.2) / 0.1 = 3 s.

For a zero-order reaction, t = [A₀] / k. Here, t = 0.5 M / 0.1 M/s = 5 s.

For d orbitals, the azimuthal quantum number l = 2.

For l=2 (d orbital), m_l can take values from -l to +l, which are -2, -1, 0, 1, 2.

For a p orbital, l=1, so m_l can take values -1, 0, +1.

The spin quantum number (m_s) can take values of -1/2 and +1/2.

For a p orbital (l=1), m_l can take values -1, 0, +1.

For l=2 (d orbital), m_l can take values from -2 to +2, which are -2, -1, 0, 1, 2.

The RMS speed increases with temperature as v_rms = sqrt(3RT/M) shows that it is directly proportional to the square root of temperature T.

According to Boyle's law, for a given mass of gas at constant temperature, the pressure is inversely proportional to the volume. Halving the volume will double the pressure.

The equation of state for an ideal gas is given by PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.

In an isobaric process, the work done is calculated using the formula W = PΔV, where P is pressure and ΔV is the change in volume.

The ideal gas law is given by the equation PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.

The Ideal Gas Law (PV = nRT) relates pressure (P), volume (V), and temperature (T) for an ideal gas.

The ideal gas law is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.

At constant temperature, Boyle's law states that the product of pressure and volume (PV) is constant, hence P1V1 = P2V2.

According to Raoult's Law, the vapor pressure of the solution is 0.75 * 100 mmHg = 75 mmHg.

Using Gauss's law, the electric field due to an infinite plane sheet of charge is E = σ/2ε₀ on either side of the sheet.

The electric field due to an infinite plane sheet of charge is constant and given by E = σ/2ε₀ on either side of the sheet.

Destructive interference occurs when the path difference is an odd multiple of λ/2 (i.e., (2n+1)λ/2).