The minimum wavelength can be calculated using the equation λ = hc/W. Substituting h = 4.14 x 10^-15 eV·s, c = 3 x 10^8 m/s, and W = 4 eV gives λ = 310 nm.

The threshold frequency can be calculated using the formula f = φ/h, where h is Planck's constant (4.14 x 10^-15 eV·s).

Heat travels through the metal rod by conduction, as the kinetic energy is transferred from one atom to another.

The needle floats because the surface tension of water creates a force that counteracts the weight of the needle.

First, calculate the work done: W = mgh = 10 kg * 9.8 m/s² * 5 m = 490 J. Then, P = W/t = 490 J / 2 s = 245 W.

First, calculate the work done: W = mgh = 10 kg * 9.8 m/s² * 5 m = 490 J. Then, power is P = W/t = 490 J / 5 s = 98 W.

First, calculate the work done: W = mgh = 10 kg * 9.8 m/s² * 2 m = 196 J. Then, power is P = W/t = 196 J / 4 s = 49 W, approximately 50 W.

The work done against gravity is W = mgh = (50 kg)(9.8 m/s²)(2 m) = 980 J. Power is P = W/t = 980 J / 5 s = 196 W, approximately 200 W.

The work done is W = mgh = 50 kg * 9.8 m/s^2 * 2 m = 980 J. Power is W/t = 980 J / 5 s = 196 W, approximately 200 W.

Work done = Force × Distance = 100 N × 2 m = 200 J. Power = Work / Time = 200 J / 4 s = 50 W.

Energy (E) = hc / λ = (1240 nm·eV) / 300 nm = 4.13 eV.

Frequency (ν) = E/h = 5 eV / (4.14 x 10^-15 eV·s) = 7.5 x 10^14 Hz.

Kinetic energy (K.E.) = Photon energy - Work function = 5 eV - 3 eV = 2 eV.

The angular momentum of a rotating planet is constant if no external torques act on it.

The total electric flux through the Gaussian surface is given by Φ = Q/ε₀, where Q is the charge enclosed.

The electric flux through a closed surface is given by Φ = Q_enc/ε₀. Here, Q_enc = Q, so Φ = Q/ε₀.

According to Gauss's law, the total electric flux through a closed surface is equal to the charge enclosed divided by ε₀, thus Φ = Q/ε₀.

Increasing the length of the wire increases the potential gradient, which can improve the accuracy of the measurement by allowing for finer adjustments.

For accurate comparison of two emfs using a potentiometer, both circuits must have the same potential gradient to ensure that the readings are directly comparable.

The potential gradient is calculated as the potential difference divided by the length of the wire: 12 V / 6 m = 2 V/m.

The EMF of the cell can be calculated as EMF = potential gradient × length = 1.5 V/m × 3 m = 4.5 V.

To measure the potential difference across a resistor, the potentiometer must be connected in parallel with the resistor.

The potential gradient is calculated as the potential difference divided by the length of the wire: 12 V / 6 m = 2 V/m.

The potential gradient is calculated as V/L = 12V/4m = 3 V/m.

Using Ohm's law, V = IR = 0.5 A * 10 ohms = 5 V.

Using Snell's law: n1 * sin(θ1) = n2 * sin(θ2). 1 * sin(30°) = 2 * sin(θ2) => sin(θ2) = 0.25 => θ2 = 15°.

A ray of light passing through the optical center of a lens continues in a straight line without bending.

Using Ohm's Law, V = I * R = 2 A * 5 Ω = 10 V.

Using Ohm's Law, R = V / I = 9 V / 3 A = 3 Ω.

The rotational kinetic energy is given by (1/2)Iω^2, where I is the moment of inertia.