Tag: science & technology

The formula for acceleration due to gravity at depth 'd' from Earth's surface is gd = g(1 - d/R), where g is surface gravity and R is Earth's radius. This shows that gravity decreases linearly as we go deeper inside Earth, becoming zero at the center.

The correct formula for kinetic energy is k = (1/2)mv², where m is mass and v is velocity. Option D correctly shows k = (1/2).m.v.v which represents mv². Option A has an extra v (v³), Option B is incomplete (0.5mv), and Option C only has mv (not squared).

The escape velocity formula is Ve = sqrt(2GM/r), where G is the gravitational constant, M is the mass of the celestial body, and r is its radius. Option C correctly shows this formula. Option A is missing M in the numerator, Option B incorrectly multiplies by r (instead of dividing), and Option D has a typo ('srt' instead of 'sqrt').

Boyle's law states that for an ideal gas at constant temperature, the pressure and volume are inversely proportional: P₁V₁ = P₂V₂. This means when pressure increases, volume decreases proportionally, and vice versa, as long as temperature remains unchanged. Option A correctly represents this relationship.

Charles's law states that for an ideal gas at constant pressure, volume is directly proportional to absolute temperature: V ∝ T, or V₁/T₁ = V₂/T₂. Cross-multiplying gives V₁T₂ = V₂T₁, which is option A. This means that as temperature increases, volume increases proportionally, and vice versa, when pressure is held constant.

Ohm's law states that the voltage across a conductor is directly proportional to the current flowing through it: V = IR, where V is voltage, I is current, and R is resistance. Option B correctly represents this relationship. Option A shows division instead of multiplication, and options C and D have nonsensical formulas.

When resistors are connected in series, the equivalent (total) resistance is the sum of all individual resistances: R_eq = R₁ + R₂ + R₃ + ... + Rₙ. This is because the same current flows through each resistor, and the total voltage drop is the sum of individual voltage drops. Option C correctly represents the general formula for any number of resistors.

The self-inductance of a solenoid is given by L = μ₀n²LA where μ₀ is permeability, n is turns per unit length, L is length, A is cross-sectional area. Option B shows the correct relationship.

Energy stored in a capacitor is E = (1/2)CV² where C is capacitance and V is voltage. Option B correctly shows v.v (v squared). The factor 1/2 arises from integrating work done in charging.

The magnetic force on a moving charge is given by F = q(v × B), whose magnitude is F = qvB sinθ where θ is the angle between velocity and magnetic field. Option B correctly shows the sine relationship.