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

The moment of inertia of a solid sphere about its center is I = 2/5 MR^2.

The period (T) is the inverse of frequency (f); T = 1/f = 1/440 ≈ 0.00227 s.

Centripetal force = m(v²/r) = 1(4²/2) = 8 N. Tension in the string = 8 N.

Centripetal force (F_c) = mv²/r. Assuming mass (m) = 1 kg, F_c = 1(4²)/2 = 8 N.

Using the first law of thermodynamics, ΔU = Q - W = 100 J - 40 J = 60 J.

Using the First Law of Thermodynamics, ΔU = Q - W = 200 J - 50 J = 150 J.

Using the first law, ΔU = Q - W = 100 J - 150 J = -50 J.

Maximum possible temperature = Measured value + Error = 25 + 0.5 = 25.5°C.

Minimum temperature = Recorded temperature - Error = 25 - 0.5 = 24.5°C.

Maximum possible temperature = Measured value + Error = 100 + 0.5 = 100.5°C.

Force = Torque / Distance = 15 Nm / 0.3 m = 50 N.

Torque = Force × Distance × sin(θ) => 25 Nm = 10 N × 5 m × sin(θ) => sin(θ) = 0.5 => θ = 30 degrees.

Force = Torque / Radius = 25 Nm / 0.5 m = 50 N.

Force = Torque / Distance = 25 Nm / 0.5 m = 50 N.

Force = Torque / Distance = 30 Nm / 3 m = 10 N.

Angular acceleration α = Torque / Moment of inertia = 5 Nm / 2 kg·m² = 2.5 rad/s².

Force = Torque / Distance = 8 Nm / 0.2 m = 40 N.

Time = distance / speed = 180 km / (72 km/h) = 2.5 h.

Range of possible volumes = 200 - 5 to 200 + 5 = 195 L to 205 L.

Maximum true weight = Measured weight + Error = 10 kg + 0.2 kg = 10.2 kg.

The distance traveled by the center of mass after one complete rotation is equal to the circumference of the wheel, which is 2πR.

Using the formula F = BIL, where B is the magnetic field, I is the current, and L is the length of the wire (1 m), F = 0.1 T * 5 A * 1 m = 0.5 N.

Using Ampere's Law, B = μ₀I/2πr, where μ₀ = 4π × 10^-7 Tm/A, we find B = (4π × 10^-7)(5)/(2π(0.1)) = 0.1 T.

The magnetic field at the center of a semicircular arc of radius R carrying current I is given by B = μ₀I/(4R).

The magnetic field at the center of a semicircular wire carrying current I is given by B = μ₀I/(4R) for the semicircle, which is half of the full circular loop.

The magnetic field at the center of a semicircular wire carrying current I is given by B = μ₀I/(4R).

Strain is defined as the change in length divided by the original length, so 2% = 0.02.

The elongation (ΔL) can be expressed as ΔL = F * L / (A * E).

Resistance is directly proportional to length; doubling the length doubles the resistance.