g = G * M / R² = (6.67 × 10^-11) * (6 × 10^24) / (6.4 × 10^6)² = 9.81 m/s²

The gravitational acceleration at the surface of the Earth is given by g = GM/R^2.

The gravitational acceleration at the surface of the Earth is given by g = GM/R^2.

The gravitational force F acting on a satellite at height h is given by F = GmM/(R+h)^2, where G is the gravitational constant.

Gravitational acceleration is directly proportional to mass, so if the mass doubles, g also doubles.

Gravitational acceleration is directly proportional to mass; thus, if the mass doubles, g also doubles.

Weight is proportional to mass; thus, if the Earth's mass doubles, the weight of an object on its surface also doubles.

F ∝ M; if M doubles, F also doubles.

F = G * (m1 * m2) / r², doubling the mass of Earth doubles the force.

If the mass of the Earth doubles, the gravitational force on an object at its surface would also double.

Weight is directly proportional to mass. If the Earth's mass doubles, the weight of the object also doubles.

If the mass of the Earth increases, the gravitational force experienced by an object on its surface would increase.

Relative error = (Absolute error / Measured value) = 0.5 / 20 = 0.025 or 2.5%

Absolute error = Relative error * Measured value = 0.02 * 100 = 2.

Relative error = Absolute error / True value. Let true value be x. 0.04 = |75 - x| / x. Solving gives x = 78.

RMS speed is inversely proportional to the square root of molar mass, so if M is doubled, v_rms decreases by sqrt(2).

The RMS speed is inversely proportional to the square root of the molar mass. If M is doubled, v_rms decreases by sqrt(2).

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

Angular momentum L = Iω = 10 kg m² * 5 rad/s = 50 kg m²/s.

Rotational kinetic energy is given by KE = 1/2 I ω² = 1/2 * 10 * 5² = 125 J.

Using τ = Iα, we have α = τ/I = 20 N·m / 10 kg·m² = 2 rad/s².

Rotational kinetic energy is given by KE = 1/2 I ω^2. If I is doubled and ω remains constant, KE also doubles.

Angular acceleration α = τ/I. If I is doubled and τ remains constant, α is halved.

Angular momentum L = Iω; if I is doubled and ω remains constant, L also doubles.

According to Newton's second law for rotation, τ = Iα, if I increases and τ is constant, α must decrease.

Damped frequency (ω_d) = ω_n√(1-ζ^2) = 5√(1-0.2^2) = 5√(0.96) ≈ 4.8 rad/s.

When the object distance equals the focal length, the image is formed at infinity.

When the object is at the focal length, the image is formed at infinity.

The average current over one complete cycle is I_avg = I_peak/√2 = 5/√2 = 2.5 A.

The RMS voltage (V_rms) is given by V_rms = V_peak / √2. Therefore, V_rms = 200 V / √2 = 141.42 V.