Using the formula τ = Iα, we have α = τ/I = 10 Nm / 2 kg·m² = 5 rad/s².

Wave speed (v) can be calculated using the formula v = fλ. Here, v = 50 Hz * 3 m = 150 m/s.

The speed of a wave can be calculated using the formula v = f × λ. Here, v = 50 Hz × 4 m = 200 m/s.

Using the wave equation v = fλ, we can rearrange it to find λ = v/f. Thus, λ = 300 m/s / 150 Hz = 2 m.

Total energy (E) in SHM is proportional to the square of the amplitude (A). If A is doubled, E becomes 4A^2, hence it quadruples.

The energy of a wave is proportional to the square of its amplitude. Therefore, if the amplitude increases, the energy also increases.

The energy carried by a wave is proportional to the square of its amplitude. Therefore, if the amplitude increases, the energy also increases.

The energy of a wave is proportional to the square of its amplitude. Therefore, if the amplitude increases, the energy also increases.

The energy carried by a wave is proportional to the square of the amplitude. Therefore, if the amplitude is tripled, the energy increases by a factor of 3^2 = 9.

Capacitance C is defined as C = Q/V. If C is doubled and Q remains constant, then V must halve to maintain the equation.

The capacitance C of a parallel plate capacitor is given by C = εA/d. If the distance d is doubled, the new capacitance will be C/2.

Capacitance C = Q/V. If Q is doubled and V remains constant, C must also double.

The electric field E between the plates of a capacitor is directly proportional to the charge. If the charge is doubled, the electric field also doubles.

Using Ohm's Law, V = I * R = 3A * 2Ω = 6V.

Using Ohm's Law, R = V / I = 6V / 2A = 3Ω.

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

The heat produced is proportional to the square of the current (H ∝ I²), so if I is doubled, heat becomes 4 times.

Using Ohm's Law, V = I * R = 5A * 10Ω = 50V.

Tensile strength is inversely proportional to the cross-sectional area. Halving the diameter reduces the area to a quarter, thus tensile strength quadruples.

If the distance d is halved, the capacitance C = εA/d will double.

If the slit separation d is halved, the angle θ for the first-order maximum (d sin θ = λ) will increase, effectively doubling the angle.

According to the inverse square law, if the distance is doubled, the force becomes 1/(2^2) = 1/4 of the original force.

According to Coulomb's law, the force F is inversely proportional to the square of the distance (F ∝ 1/r^2). If r is tripled, F becomes 1/9 of its original value.

Increasing the distance from the slits to the screen increases the fringe width, as fringe width β is proportional to the distance.

The potential difference (V) between the plates is given by V = Ed, where E is the electric field and d is the distance between the plates.

The period T is inversely proportional to frequency f. If f is doubled, T is halved.

The time period (T) is the reciprocal of frequency (f). Therefore, T = 1/f = 1/50 Hz = 0.02 s.

Inductive reactance (X_L) is directly proportional to frequency (f). Therefore, if frequency increases, X_L decreases.

Inductive reactance (X_L) is given by X_L = 2πfL. If the inductance (L) is doubled, X_L will also double.

Resistance (R) is directly proportional to length (L). If length is doubled, resistance also doubles.