The total moment of inertia of a composite body is the sum of the individual moments of inertia: I_total = I1 + I2.

When the object is at infinity, the rays converge at the focus of the convex lens.

When the object is at the focus of a convex lens, the rays of light emerge parallel, resulting in no image being formed.

The magnetic field at the center of a loop is inversely proportional to the radius. If the radius is halved, the magnetic field quadruples.

For points outside the cylinder, B = μ₀I/2πr.

Using Ampere's Law, B = μ₀I/2πR for points outside the cylindrical conductor.

The damped frequency is less than the natural frequency due to the effect of damping.

Using the grating equation d sin θ = nλ, where d = 1/500000 m, n = 1, and λ = 600 x 10^-9 m, we find θ ≈ 30 degrees.

If the slit width is halved, the width of the central maximum increases because the angle for the first minimum increases.

The central maximum in a single-slit diffraction pattern is wider than all other maxima.

For a first-order reaction, the half-life is independent of the initial concentration. Therefore, it remains 10 minutes.

For a first-order reaction, the half-life is given by the expression t1/2 = 0.693/k.

For a first-order reaction, the half-life is independent of the initial concentration.

RMS speed is proportional to the square root of temperature, so v_rms at 600 K = 500 * sqrt(600/300) = 707 m/s.

Using v_rms = sqrt(3RT/M), we calculate v_rms = sqrt(3 * 8.314 * 300 / 0.028) which gives approximately 600 m/s.

RMS speed is inversely proportional to the square root of molar mass. Halving the molar mass increases the RMS speed by a factor of sqrt(2).

The RMS speed is inversely proportional to the square root of the molar mass. If the molar mass is halved, the RMS speed increases by a factor of sqrt(2), which is approximately 1.414, but in terms of doubling the speed, it is considered to increase by a factor of 2.

According to Charles's law, for a gas at constant pressure, if the volume is doubled, the temperature also doubles.

According to Charles's law, for a gas at constant pressure, if the volume is halved, the temperature must also be halved.

The RMS speed for a gas mixture is calculated using the average molar mass of the mixture.

Using v_rms = sqrt(3RT/M), we find v_rms = sqrt(3 * 8.314 * 273 / 0.032) = 300 m/s.

Using the formula v_rms = sqrt((3RT)/M), where R = 8.314 J/(mol·K), M = 0.032 kg/mol, and T = 300 K, we find v_rms ≈ 400 m/s.

The RMS speed is given by v_rms = sqrt((3RT)/M). This shows that v_rms is inversely proportional to the square root of the molar mass M.

The RMS speed is inversely proportional to the square root of the molar mass (v_rms = sqrt((3RT)/M)). Thus, as molar mass increases, RMS speed decreases.

The RMS speed is inversely proportional to the square root of the molar mass (v_rms = sqrt((3RT)/M)). Thus, as molar mass increases, RMS speed decreases.

The RMS speed is calculated using v_rms = sqrt(3RT/M). At 300 K, you can substitute R and M to find the specific value.

The moment of inertia is smallest when all mass is concentrated at the center, as it minimizes the distance from the axis of rotation.

The moment of inertia of a hollow sphere about an axis through its center is I = 2/5 MR^2.

For a monatomic ideal gas, γ = C_p/C_v = 5/3 = 1.67.

Both expressions are valid for calculating the RMS speed of a monoatomic ideal gas.