Universal Law of Gravitation: NEET MCQs with Answers

Explanation: Initial: F = Gm₁m₂/r². New: F' = G(2m₁)(2m₂)/(2r)² = 4Gm₁m₂/4r² = Gm₁m₂/r² = F. Doubling both masses (factor of 4) and doubling distance (factor of 4 denominator) cancel out, leaving the force unchanged.

Explanation: Due to symmetry, the gravitational field from each mass at the center points toward that mass. The four forces are equal in magnitude and directed toward the four corners. By vector addition, they cancel perfectly, resulting in zero net field at the center. This is a consequence of the square's fourfold rotational symmetry.

Explanation: Since F ∝ 1/r², when r becomes 2r, then F_new = F_old/2² = F_old/4. The inverse-square relationship means that doubling the distance reduces the force to one-quarter. This principle is crucial in understanding planetary orbits and satellite motion.

Explanation: Newton's law of gravitation shows that gravitational force depends only on masses and their separation (F = Gm₁m₂/r²). It is completely independent of relative velocity, relative motion, the nature of any material between the masses, or any other factor except mass and distance.

Explanation: G is a universal constant with value 6.67 × 10⁻¹¹ N·m²/kg². It is independent of the nature, size, or separation of masses. This universality shows that gravity is a fundamental interaction that operates identically everywhere in the cosmos.

Explanation: Newton's law of universal gravitation: F = Gm₁m₂/r². The force decreases with the square of the distance, not linearly or cubically. This inverse-square law is fundamental to gravitation and applies to all massive objects in the universe.

Explanation: Resultant force = √3·GM²/a² at radius a/√3. Centripetal force: mv²/r = √3·GM²/a² gives v² = GM/a.

Explanation: By symmetry, field from each points toward corner. Four equal vectors toward corners cancel. Superposition principle applied.

Explanation: F = Gm(M-m)/d². For maximum, dF/dm = 0 gives M - 2m = 0, so m = M/2. Product m(M-m) maximized when both parts equal.

Explanation: F = Gm₁m₂/r² = (6.67 × 10⁻¹¹ × 50 × 50)/1² = 1.67 × 10⁻⁷ N.

Explanation: Unlike electric forces, gravity is always attractive. Depends only on masses and distance, not relative velocity or medium.

Explanation: F ∝ 1/r². When r → 2r, F_new = F_old/4. Inverse-square law fundamental to gravitation.

Explanation: Gravitational field intensity I = F/m, where F is the force on a mass m placed at that point. It has units of N/kg or m/s² and represents the strength of the gravitational field. This is analogous to electric field intensity in electrostatics.

Explanation: G is universal constant in F = Gm₁m₂/r², same everywhere in universe. Other values are g, c, and e respectively.

Explanation: F = Gm₁m₂/r² shows force is proportional to product of masses and inversely proportional to square of distance. This is the mathematical statement of universal gravitation.