Centripetal acceleration (a_c) = v²/r. First find v = 2πr/T = 2π(4)/8 = π m/s. Then a_c = (π)²/4 = 2.5 m/s².

Angular momentum L = mvr; if v is doubled, L also doubles.

Work done = Force × Distance = 12 N × 3 m = 36 J.

Work done = Force × Distance = 3 N × 6 m = 18 J.

Final kinetic energy = Initial kinetic energy + Work done = 100 J + 50 J = 150 J.

Angular momentum is constant as the particle moves with constant velocity.

The angular momentum is non-zero and depends on the distance from the point to the line of motion.

Angular momentum L = mvr, where r is the perpendicular distance from the line of motion to point P.

Final velocity (v) = u + at = 3 + (2 * 5) = 13 m/s.

Using the formula: final velocity = initial velocity + acceleration * time. Final velocity = 2 + 4 * 5 = 22 m/s.

Final velocity = initial velocity + (acceleration * time) = 10 m/s + (2 m/s² * 5 s) = 20 m/s.

The moment of inertia of a point mass is given by I = mr^2.

The moment of inertia of a point mass about an axis is given by I = mr^2.

Angular momentum L = mvr, where v is the linear speed and r is the radius.

The magnetic force acting on a charged particle moving in a magnetic field is given by F = qvB sin(θ), where θ is the angle between the velocity vector and the magnetic field vector.

Relative uncertainty = (Uncertainty / Measured value) * 100 = (0.1 / 2.0) * 100 = 5%.

Using conservation of energy, potential energy at the top = kinetic energy at the bottom. mgh = 0.5mv². Solving gives v = sqrt(2gh) = sqrt(2 * 9.8 * 1) = 4.4 m/s.

The period of a simple pendulum is given by T = 2π√(L/g). If L is doubled, T becomes T' = 2π√(2L/g) = √2 * T ≈ 1.41 s.

Using conservation of energy, potential energy at the top = kinetic energy at the bottom. mgh = 0.5mv². Solving gives v = √(2gh) = √(2 * 9.8 * 2) = 4 m/s.

Using conservation of energy, potential energy at the top = kinetic energy at the bottom. mgh = 0.5mv^2. Solving gives v = sqrt(2gh) = sqrt(2*9.8*5) = 10 m/s.

The period T of a simple pendulum is given by T = 2π√(L/g). Here, L = 1 m and g = 9.8 m/s². Thus, T = 2π√(1/9.8) ≈ 2.0 s.

The period T of a simple pendulum is given by T = 2π√(L/g). If L is doubled, T becomes T' = 2π√(2L/g) = √2 * T = 1.41 s.

The period of a pendulum is given by T = 2π√(L/g). If L is increased to 4L, T becomes 2π√(4L/g) = 2T = 2 seconds.

The period T = 2π√(L/g). If L is increased by a factor of 4, T increases by a factor of √4 = 2.

The period T = 2π√(L/g). If L is tripled, T becomes √3 times longer, so T = 2 s.

Length L = (gT^2)/(4π^2) = (9.8 * 1^2)/(4 * π^2) ≈ 1 m.

Angular frequency (ω) = 2π/T = 2π/1.5 = 4π/3 rad/s.

Frequency (f) is the reciprocal of the period (T). Therefore, f = 1/T = 1/2 = 0.5 Hz.

The period T of a simple pendulum is given by T = 2π√(L/g). Rearranging gives L = (T²g)/(4π²). Using g = 9.8 m/s², L = (2² * 9.8)/(4π²) ≈ 1 m.

The period T of a simple pendulum is given by T = 2π√(L/g). For length 4L, T' = 2π√(4L/g) = 2T.