Linear velocity v = rω; if r is halved and ω remains constant, v is halved.

The moment of inertia of a solid disk is I = 1/2 MR^2. If R is doubled, I becomes 1/2 M(2R)^2 = 2MR^2, which is 4 times the original.

The electric field E due to a point charge decreases with the square of the distance from the charge, so if the radius is doubled, the electric field halves.

The electric field E due to a point charge decreases with the square of the distance from the charge, so if the radius is doubled, the electric field halves.

The electric field due to a point charge is independent of the radius of the Gaussian surface; it remains the same.

The focal length f of a mirror is given by f = R/2. Thus, f = 40 cm / 2 = 20 cm.

The focal length f of a mirror is given by f = R/2. For a convex mirror, R = 30 cm, so f = 30/2 = 15 cm.

Using the lens maker's formula, f = R/(n-1) = 20/(1.5-1) = 40 cm.

Using the lens maker's formula, f = R/(n-1) = 30/(1.5-1) = 30/0.5 = 60 cm.

Using the lens maker's formula, f = R/(n-1) = 30/(1.5-1) = 30/0.5 = 60 cm.

Focal length f = R/2 = 30 cm / 2 = 15 cm.

The focal length (f) of a spherical mirror is given by f = R/2. Here, R = 40 cm, so f = 40/2 = 20 cm.

The distance from the center of the Earth to a geostationary satellite is approximately 42000 km.

Gravitational force is inversely proportional to the square of the radius. If the radius is doubled, the force becomes 1/4 of the original.

g = G * M / R²; if R is doubled, g becomes g/4.

The orbital speed v of a satellite is given by v = sqrt(GM/(R+h)), where M is the mass of the Earth and G is the gravitational constant.

A geostationary satellite orbits at a height of approximately 36,000 km above the Earth's surface, which is about R (the radius of the Earth) plus the height of the satellite.

The gravitational force acting on the satellite is given by Newton's law of gravitation, which states that F = G * (M * m) / (R + h)^2, where M is the mass of the Earth and m is the mass of the satellite.

At a height R above the Earth's surface, the gravitational acceleration is g/4, derived from the formula g' = g(R/(R+h))^2.

The radius of a geostationary orbit is approximately 3R, where R is the radius of the Earth.

The gravitational force is inversely proportional to the square of the distance. If the radius doubles, the force decreases to one-fourth.

Gravitational acceleration is inversely proportional to the square of the radius, so it would be quartered.

Weight is proportional to 1/r^2; if the radius doubles, the weight becomes four times less.

Gravitational acceleration is inversely proportional to the square of the radius. If the radius doubles, g becomes 1/(2^2) = 1/4 of the original value.

Gravitational acceleration is inversely proportional to the square of the radius. If the radius is halved, g becomes 4 times greater.

The orbital speed v is given by v = √(GM/r). If r is doubled, v decreases by a factor of √2.

Range = Maximum - Minimum. Therefore, Maximum = Range + Minimum = 15 + 5 = 20.

Using the Arrhenius equation, a rule of thumb states that for every 10°C increase in temperature, the rate doubles if Ea is around 40 kJ/mol.

Induced EMF (ε) = -L(dI/dt) = -3 H * 2 A/s = -6 V.

Critical angle θc = sin⁻¹(1/1.33) ≈ 48.6°.