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.

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

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

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.

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

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

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°.