The RMS speed increases with the square root of the temperature. Therefore, at 600 K, the RMS speed will be 400 * sqrt(2), which is approximately 800 m/s.

Kinetic energy per molecule = (1/2)mv^2. Using v = 400 m/s and m = M/N_A, we find KE = 0.5 mJ.

The average speed is related to RMS speed by the relation v_avg = (2/3) * v_rms. Thus, v_avg = (2/3) * 400 = 267 m/s.

The average speed of gas molecules is approximately 0.8 times the RMS speed, so average speed = 0.8 * 400 m/s = 320 m/s.

The speed at 1/2 of the RMS speed is simply 500 m/s / 2 = 250 m/s.

The average speed of gas molecules is related to the RMS speed by the relation v_avg = (v_rms * sqrt(8/3)). Therefore, the average speed is approximately 400 m/s.

The RMS speed is an average measure; individual molecular speeds will vary around this value.

Using v_rms = sqrt(3RT/M), we rearrange to find T = (v_rms^2 * M) / (3R). Plugging in values gives T approximately 300 K.

When the slit width is equal to the wavelength, a wide central maximum is observed due to significant diffraction.

If the slit width is halved, the width of the central maximum doubles, as it is inversely proportional to the slit width.

Halving the slit width increases the angular width of the central maximum, making it double.

Frequency f = v/λ = 300 m/s / 3 m = 100 Hz.

Centripetal acceleration a_c = v²/r. If v is doubled, a_c increases by a factor of 4.

Speed of light in medium = c/n = (3 x 10^8 m/s) / 1.5 = 2 x 10^8 m/s.

Stress = Young's modulus × Strain = 150 GPa × 0.01 = 150 MPa.

According to Hooke's Law, if stress is doubled, strain also doubles for elastic materials.

Increasing the supply voltage does not affect the balance condition; it remains dependent on the resistance ratios.

Force = Surface Tension × Length = 0.072 N/m × 0.5 m = 0.036 N.

According to Newton's law of cooling, the rate of heat transfer increases with an increase in temperature difference.

Maximum possible temperature = Measured value + Error = 30 + 0.5 = 30.5°C

For most conductors, resistivity increases with temperature due to increased atomic vibrations.

According to Gay-Lussac's Law, if the temperature of a gas is increased while keeping the volume constant, the pressure will also increase proportionally, thus it doubles.

The RMS speed is proportional to the square root of the temperature. If the temperature is doubled, the RMS speed increases by a factor of sqrt(2).

The RMS speed is proportional to the square root of the temperature. If the temperature is doubled, the RMS speed increases by a factor of sqrt(2).

RMS speed is directly proportional to the square root of temperature. Halving the temperature results in a decrease in RMS speed by sqrt(2).

According to Gay-Lussac's Law, if the temperature of a gas increases at constant volume, the pressure increases.

RMS speed increases by sqrt(4) = 2, since v_rms is proportional to sqrt(T).

RMS speed is proportional to the square root of temperature. Increasing from 300 K to 600 K increases the speed by sqrt(2).

According to Gay-Lussac's Law, if the temperature of a gas is increased while keeping the volume constant, the pressure increases.

The viscosity of a liquid generally decreases with an increase in temperature.