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.

Average induced emf = -ΔΦ/Δt = -(0.2 - 0.5)/2 = 0.15 V = 150 V.

An induced EMF is generated when there is a change in magnetic flux through a coil.

If the mass of the Earth doubles, the acceleration due to gravity also doubles, as it is directly proportional to mass.

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

The energy stored in a capacitor is given by U = 1/2 CV^2. If V is halved, the energy becomes U' = 1/2 C(V/2)^2 = 1/8 CV^2, which is halved.

The charge (Q) stored in a capacitor is directly proportional to the potential difference (V) across it, given by Q = CV.

Work done (W) = Charge (Q) × Potential difference (V) = 2 C × 10 V = 20 J.

Linear velocity v = rω, so if r is halved and ω remains constant, v also halves.

The focal length (f) of a concave mirror is given by f = R/2, where R is the radius of curvature. Thus, f = 20 cm / 2 = 10 cm.

The focal length f of a lens is given by f = R/2. Therefore, f = 20 cm / 2 = 10 cm.

The focal length (f) of a mirror is given by f = R/2. For a convex mirror, R is positive, so f = 20 cm / 2 = 10 cm.

According to Ohm's Law, if the resistance (R) is doubled and the voltage (V) remains constant, the current (I) will be halved (I = V/R).

The peak voltage (V_peak) is calculated as V_peak = V_rms × √2 = 100 V × √2 ≈ 141.42 V.

According to Ohm's law, if voltage increases and resistance remains constant, current will also increase proportionally.

Inductive reactance (X_L) is given by X_L = V/I. Here, X_L = 100 V / 2 A = 50 Ω.

The electric fields due to both charges at the midpoint cancel each other out, resulting in a net electric field of 0 N/C.

Total resistance R = 4Ω + 12Ω = 16Ω. Voltage V = I * R = 2A * 16Ω = 32V.

Using the formula for parallel resistors, 1/R_eq = 1/R1 + 1/R2 = 1/4 + 1/6 = 5/12, R_eq = 12/5 = 2.4Ω.