Acceleration = F/m = 30 N / 10 kg = 3 m/s². Final velocity = initial velocity + (acceleration × time) = 0 + (3 m/s² × 3 s) = 9 m/s.

Potential Energy (PE) = m * g * h = 10 kg * 10 m/s² * 20 m = 2000 J

Total Mechanical Energy = Kinetic Energy + Potential Energy = (1/2 * 10 kg * (4 m/s)²) + (10 kg * 9.8 m/s² * 5 m) = 80 J + 490 J = 570 J

Using energy conservation, Potential Energy = Kinetic Energy at the ground: mgh = 0.5 mv^2; v = sqrt(2gh) = sqrt(2 * 10 m/s² * 20 m) = 20 m/s

The force acting on it is its weight, F = mg = 2 kg × 10 m/s² = 20 N.

Using the formula v = √(2gh) = √(2 * 10 m/s² * 20 m) = √400 = 20 m/s

Momentum (p) = m * v = 2 kg * 4 m/s = 8 kg m/s

Momentum (p) = mv = 3 kg * 6 m/s = 18 kg m/s

Using F = ma, a = F/m = 12 N / 3 kg = 4 m/s².

Momentum = mass × velocity = 5 kg × 4 m/s = 20 kg m/s.

Net force = Applied force - Frictional force = 20 N - 5 N = 15 N. Using F = ma, a = F/m = 15 N / 5 kg = 3 m/s².

Capacitance C is given by C = Q/V. Here, C = 24μC / 12V = 2μF.

The capacitance C is defined as C = Q/V.

When the distance is doubled, the potential difference across the capacitor also doubles, resulting in 24V.

The charge Q stored in a capacitor is given by Q = CV.

Work Done = Change in Kinetic Energy = 1/2 * m * (v^2 - u^2) = 1/2 * 1000 kg * (20 m/s)^2 = 200,000 J

Force F = qE = (1 × 10^-6 C)(1000 N/C) = 0.001 N.

The force on a negative charge is in the direction opposite to the electric field, hence towards the positive charge.

First, find the equivalent resistance R_eq = 1/(1/4 + 1/6) = 2.4Ω. Then, I = V/R_eq = 12V/2.4Ω = 5 A.

Using Ohm's Law, V = I * R = 2A * 6Ω = 12V.

The magnetic field lines around a circular loop of wire are concentric circles centered on the axis of the loop.

Kinetic Energy is proportional to the square of the speed. If speed is doubled, KE increases by a factor of 2^2 = 4.

Using F = ma, a = F/m = 50 N / 25 kg = 2 m/s².

The magnetic dipole moment (μ) is defined as the product of the current (I) flowing through a loop and the area (A) of the loop, μ = I × A.

Frequency (f) = (1/2π)√(k/m) => k = (2πf)² * m = (2π*3)² * 2 ≈ 18 N/m.

Frequency (f) = 1/(2π)√(k/m) => k = (2πf)²m = (2π × 3)² × 0.5 ≈ 18 N/m.

Period (T) = 1 / frequency = 1 / 2 Hz = 0.5 s.

Capacitance C is inversely proportional to the distance d between the plates. If d is halved, C doubles, so the new capacitance is 10μF.

Time period (T) = 2π√(L/g) = 2π√(1/9.8) ≈ 2 s

A plane mirror always produces a virtual and erect image, which is the same size as the object.