The disk has a smaller moment of inertia than the ring, resulting in greater acceleration down the incline.

A diverging lens always forms a virtual and upright image when the object is placed in front of it.

Using the formula α = (ω - ω₀)/t, we have α = (0 - 30 rad/s) / 10 s = -3 rad/s².

Rotational kinetic energy K.E. = (1/2)Iω² = (1/2)(2)(10)² = 100 J.

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 = 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.

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.

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.

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

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

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

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

Using conservation of energy, potential energy at the top = kinetic energy at the bottom. The total kinetic energy is the sum of translational and rotational kinetic energy. Thus, v = √(5gh/7).

Using the formula λ = v/f, where v is the speed and f is the frequency, we have λ = 340 m/s / 1700 Hz = 0.2 m.

Potential Energy (PE) = 1/2 * k * x^2 = 1/2 * 200 N/m * (0.1 m)^2 = 1 J

Potential Energy in Spring (PE) = 1/2 kx^2 = 1/2 * 500 N/m * (0.2 m)^2 = 10 J

Using the equation of motion: h = ut + 0.5gt². Solving for t gives t ≈ 4 seconds.