Acceleration = Force / Mass = 100 N / 50 kg = 2 m/s².

Using F = ma, a = F/m = 100 N / 50 kg = 2 m/s².

Using F = ma, a = F/m = 30 N / 3 kg = 10 m/s².

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

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

A negative focal length indicates that the lens is a concave lens.

Power (P) of a lens is given by P = 1/f (in meters). Here, f = 15 cm = 0.15 m, so P = 1/0.15 = +6.67 D.

According to the law of reflection, the angle of reflection is equal to the angle of incidence. Therefore, the angle of reflection is also 30 degrees.

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.

A magnetic field is produced by moving electric charges, such as those in a current-carrying wire.

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.

Poisson's ratio (ν) = - (lateral strain) / (longitudinal strain), thus the lateral contraction ratio is 0.3.

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.

Using the formula: H = (u² * sin²θ) / (2g). H = (20² * (1/2)) / (2 * 9.8) = 10.2 m, approximately 10 m.

When a ray passes through the center of curvature, it reflects back on itself, forming a real and inverted image at the same distance as the object.

Using Snell's law, n1 * sin(i) = n2 * sin(r). Here, n1 = 1 (air), i = 30 degrees, n2 = 1.5 (glass). Therefore, sin(r) = (1 * sin(30))/1.5 = 0.333. Thus, r = sin^(-1)(0.333) ≈ 19.5 degrees, which is approximately 20 degrees.

According to the law of reflection, the angle of reflection is equal to the angle of incidence. Therefore, the angle of reflection is 30 degrees.

New angular momentum L' = I'ω' = (2I)(ω/2) = L.

Angular momentum L is given by L = Iω, thus ω = L/I.

The rotational kinetic energy is given by KE = 0.5 I ω² = 0.5 * 3 * (4)² = 24 J.

The rotational kinetic energy is given by KE = (1/2)Iω² = (1/2)(5 kg·m²)(4 rad/s)² = 40 J.

All the given expressions represent the centripetal force acting on the satellite in different forms.

For a satellite in a stable orbit, the gravitational force provides the necessary centripetal force, hence they are equal.

The solid cylinder has a lower moment of inertia, thus it accelerates faster and reaches the ground first.

The solid cylinder has a smaller moment of inertia compared to the hollow cylinder, thus it accelerates faster and reaches the bottom first.

The solid sphere has a smaller moment of inertia compared to the hollow sphere, allowing it to accelerate faster down the incline.