This question tests understanding of how gravitational and electric forces compare in magnitude and direction for macroscopic charged objects. Both gravitational force (F = Gm₁m₂/r²) and electric force (F = k|q₁q₂|/r²) follow inverse square laws, decreasing with the square of the distance between objects, but they differ dramatically in strength: the Coulomb constant k = 9.0 × 10⁹ N·m²/C² is about 10²⁰ times larger than the gravitational constant G = 6.67 × 10⁻¹¹ N·m²/kg², making electric forces intrinsically much stronger than gravitational forces for comparable numerical values; additionally, gravity is always attractive while electric force can be attractive (opposite charges) or repulsive (same charges), and gravity depends on mass while electric force depends on charge. For the given objects with same-sign charges, electric force is repulsive and much larger (≈ 0.1 N) than gravitational attraction (≈ 3.7 × $10^{-8}$ N), with ratio ≈ 2.7 × $10^6$. Choice B is correct because it accurately identifies gravity as attractive, electric as repulsive, and electric much larger. Choice A incorrectly claims gravitational force is larger, when actually electric force dominates due to the charges and intrinsic strength difference. When comparing gravitational and electric forces: (1) both follow inverse square laws F ∝ 1/r², so distance affects them equally, (2) the ratio of strengths F_elec/F_grav = (kq₁q₂)/(Gm₁m₂) depends on charges and masses but not distance, (3) electric force is intrinsically stronger by a factor of k/G ≈ 10²⁰ when comparing equal numerical values, (4) at atomic scales electric dominates because particles have charge but tiny mass (gravity ≈ 10⁻⁴⁷ N is negligible), and (5) at cosmic scales gravity dominates because objects are massive but electrically neutral (equal + and - charges cancel, so net F_elec ≈ 0). Practical implications: chemistry, molecular biology, material strength, friction, and essentially all everyday phenomena (except falling) are determined by electric forces between atoms and molecules, while planetary orbits, tides, satellite motion, and the large-scale structure of the universe are determined by gravitational forces—the electric force's dominance at small scales is why a charged balloon can lift paper against Earth's entire gravitational pull, yet gravity's dominance at large scales is why planets orbit stars despite any residual electric charges they might have.

This question tests understanding of how gravitational and electric forces compare in magnitude and significance at different scales. Both gravitational force (F = Gm₁m₂/r²) and electric force (F = kq₁q₂/r²) follow inverse square laws, decreasing with the square of the distance between objects, but they differ dramatically in strength: the Coulomb constant k = 9.0 × 10⁹ N·m²/C² is about 10²⁰ times larger than the gravitational constant G = 6.67 × 10⁻¹¹ N·m²/kg², making electric forces intrinsically much stronger than gravitational forces for comparable numerical values. Additionally, gravity is always attractive (masses always pull together) while electric force can be attractive (opposite charges) or repulsive (same charges), and gravity depends on mass while electric force depends on charge. For scale dependence: The ratio F_elec/F_grav = (kq₁q₂)/(Gm₁m₂) is independent of distance r (since both forces have r² in denominator which cancels in the ratio), meaning the relative strength depends only on the charge-to-mass ratios of the objects—this is why electric forces dominate at atomic scales (where charge-to-mass ratio is high for particles like electrons) while gravity dominates at cosmic scales (where objects are electrically neutral with charge-to-mass ratio near zero, but masses are enormous). Choice A is correct because it properly applies both force formulas and compares the resulting magnitudes. Choice D incorrectly claims that the distance dependence is different for the two forces (claiming one decreases faster with distance than the other), when actually both follow inverse square laws (F ∝ 1/r²) and decrease at the same rate with distance—the ratio F_elec/F_grav = (kq₁q₂)/(Gm₁m₂) is independent of r. When comparing gravitational and electric forces: (1) both follow inverse square laws F ∝ 1/r², so distance affects them equally, (2) the ratio of strengths F_elec/F_grav = (kq₁q₂)/(Gm₁m₂) depends on charges and masses but not distance, (3) electric force is intrinsically stronger by a factor of k/G ≈ 10²⁰ when comparing equal numerical values, (4) at atomic scales electric dominates because particles have charge but tiny mass (gravity ≈ 10⁻⁴⁷ N is negligible), and (5) at cosmic scales gravity dominates because objects are massive but electrically neutral (equal + and - charges cancel, so net F_elec ≈ 0). Practical implications: chemistry, molecular biology, material strength, friction, and essentially all everyday phenomena (except falling) are determined by electric forces between atoms and molecules, while planetary orbits, tides, satellite motion, and the large-scale structure of the universe are determined by gravitational forces—the electric force's dominance at small scales is why a charged balloon can lift paper against Earth's entire gravitational pull, yet gravity's dominance at large scales is why planets orbit stars despite any residual electric charges they might have.

This question tests understanding of how gravitational and electric forces compare in magnitude and significance at different scales. Both gravitational force (F = Gm₁m₂/r²) and electric force (F = kq₁q₂/r²) follow inverse square laws, decreasing with the square of the distance between objects, but they differ dramatically in strength: the Coulomb constant k = 9.0 × 10⁹ N·m²/C² is about 10²⁰ times larger than the gravitational constant G = 6.67 × 10⁻¹¹ N·m²/kg², making electric forces intrinsically much stronger than gravitational forces for comparable numerical values. For equal magnitude forces, we need |F_elec| = F_grav, which gives kq²/r² = Gm²/r² (using identical spheres with mass m and charge magnitude |q|), simplifying to kq² = Gm², so q² = Gm²/k = (6.67×10⁻¹¹)(10)²/(9.0×10⁹) = (6.67×10⁻¹¹)(100)/(9.0×10⁹) = 7.41×10⁻¹⁹, giving |q| = √(7.41×10⁻¹⁹) = 8.61×10⁻¹⁰ C ≈ 8.6×10⁻¹⁰ C. Choice A is correct because it properly calculates the charge needed for force balance: |q| = m√(G/k) = 10√(6.67×10⁻¹¹/9.0×10⁹) ≈ 8.6×10⁻¹⁰ C, which is about 0.86 nanocoulombs—this tiny charge (about 5.4 billion elementary charges) on 10 kg masses produces electric force equal to their gravitational attraction, demonstrating how much stronger electric force is intrinsically. Choice B suggests |q| ≈ 8.6×10⁻⁵ C, which is 100,000 times too large—with this charge, the electric force would be 10¹⁰ times stronger than gravity, not equal to it, likely from an error in handling the square root or powers of 10 in the calculation. When comparing gravitational and electric forces: (1) both follow inverse square laws F ∝ 1/r², so distance cancels when setting forces equal, (2) the charge needed for balance is q = m√(G/k), independent of separation distance, (3) this charge scales linearly with mass (double the mass requires double the charge), (4) the tiny charge required (nanocoulombs for kilogram masses) shows electric force's enormous strength advantage, and (5) this explains why static electricity effects are so noticeable—even tiny charge imbalances create forces comparable to or exceeding gravity. The key insight is that achieving force balance requires only minuscule charges because k/G ≈ 10²⁰—this ratio appears as a square root in the charge formula, giving a factor of 10¹⁰, meaning you need only about 10⁻¹⁰ C of charge per kilogram of mass to balance gravity, which is why rubbing a balloon to transfer a tiny fraction of electrons can make it stick to a wall against Earth's entire gravitational pull.

This question tests understanding of how gravitational and electric forces compare in magnitude and significance at different scales. Both gravitational force (F = Gm₁m₂/r²) and electric force (F = kq₁q₂/r²) follow inverse square laws, decreasing with the square of the distance between objects, but they differ dramatically in strength: the Coulomb constant k = 9.0 × 10⁹ N·m²/C² is about 10²⁰ times larger than the gravitational constant G = 6.67 × 10⁻¹¹ N·m²/kg², making electric forces intrinsically much stronger than gravitational forces for comparable numerical values. Additionally, gravity is always attractive (masses always pull together) while electric force can be attractive (opposite charges) or repulsive (same charges), and gravity depends on mass while electric force depends on charge. For two protons at r=1e-15 m, F_grav = G m_$p^2$ / $r^2$ = $(6.67e-11)(1.67e-27)^2$ / $(1e-15)^2$ ≈ (6.67e-11)(2.79e-54) / 1e-30 ≈1.86e-64 /1e-30 ≈1.86e-34 N, F_elec = k q_$p^2$ / $r^2$ = (9e9)(2.56e-38) /1e-30 =2.304e-28 /1e-30 =2.304e2 N, ratio =2.304e2 /1.86e-34 ≈1.24e36, ≈1.2e36. Choice A is correct because it properly calculates the ratio (kq₁q₂)/(Gm₁m₂) with correct scientific notation. Choice B inverts the ratio, calculating F_grav/F_elec instead of F_elec/F_grav, which gives a tiny number like $10^{-36}$ instead of the enormous ratio $10^{36}$, incorrectly suggesting gravity is stronger when actually electric force is vastly stronger at this scale. When comparing gravitational and electric forces: (1) both follow inverse square laws F ∝ 1/r², so distance affects them equally, (2) the ratio of strengths F_elec/F_grav = (kq₁q₂)/(Gm₁m₂) depends on charges and masses but not distance, (3) electric force is intrinsically stronger by a factor of k/G ≈ 10²⁰ when comparing equal numerical values, (4) at atomic scales electric dominates because particles have charge but tiny mass (gravity ≈ 10⁻⁴⁷ N is negligible), and (5) at cosmic scales gravity dominates because objects are massive but electrically neutral (equal + and - charges cancel, so net F_elec ≈ 0). Practical implications: chemistry, molecular biology, material strength, friction, and essentially all everyday phenomena (except falling) are determined by electric forces between atoms and molecules, while planetary orbits, tides, satellite motion, and the large-scale structure of the universe are determined by gravitational forces—the electric force's dominance at small scales is why a charged balloon can lift paper against Earth's entire gravitational pull, yet gravity's dominance at large scales is why planets orbit stars despite any residual electric charges they might have.

This question tests understanding of how to equate gravitational and electric force magnitudes for macroscopic objects. Both gravitational force (F = Gm₁m₂/r²) and electric force (F = k|q₁q₂|/r²) follow inverse square laws, decreasing with the square of the distance between objects, but they differ dramatically in strength: the Coulomb constant k = 9.0 × 10⁹ N·m²/C² is about 10²⁰ times larger than the gravitational constant G = 6.67 × 10⁻¹¹ N·m²/kg², making electric forces intrinsically much stronger than gravitational forces for comparable numerical values; additionally, gravity is always attractive while electric force can be attractive or repulsive, and gravity depends on mass while electric force depends on charge. Setting F_elec = F_grav gives k q² / r² = G m² / r², so q² = (G m²)/k, yielding q ≈ 2.7 × 10⁻¹⁰ C for the given parameters—this tiny charge equalizes the forces because k >> G. Choice C is correct because it properly calculates q from equating the force expressions. Choice B has an error in the power of 10, reporting q as $10^{-6}$ instead of the correct $10^{-10}$, likely from incorrectly handling exponents when dividing powers of 10 in the calculation: G/k ≈ $10^{-11}$$/10^9$ = $10^{-20}$, sqrt(m² * $10^{-20}$) = m * $10^{-10}$. When comparing gravitational and electric forces: (1) both follow inverse square laws F ∝ 1/r², so distance affects them equally, (2) the ratio of strengths F_elec/F_grav = (kq₁q₂)/(Gm₁m₂) depends on charges and masses but not distance, (3) electric force is intrinsically stronger by a factor of k/G ≈ 10²⁰ when comparing equal numerical values, (4) at atomic scales electric dominates because particles have charge but tiny mass (gravity ≈ 10⁻⁴⁷ N is negligible), and (5) at cosmic scales gravity dominates because objects are massive but electrically neutral (equal + and - charges cancel, so net F_elec ≈ 0). The key insight is that electric force is far stronger intrinsically (k >> G by 10²⁰), yet gravity controls the cosmos—this apparent paradox resolves when you realize that charge comes in two types (+ and -) that cancel when combined, while mass comes in only one type (positive) that always adds up, so large objects like planets inevitably have huge total mass but near-zero net charge, making F_grav enormous while F_elec ≈ 0.

This question tests understanding of how gravitational and electric forces compare in magnitude and significance at different scales. Both gravitational force (F = Gm₁m₂/r²) and electric force (F = kq₁q₂/r²) follow inverse square laws, decreasing with the square of the distance between objects, but they differ dramatically in strength: the Coulomb constant k = 9.0 × 10⁹ N·m²/C² is about 10²⁰ times larger than the gravitational constant G = 6.67 × 10⁻¹¹ N·m²/kg², making electric forces intrinsically much stronger than gravitational forces for comparable numerical values. Additionally, gravity is always attractive (masses always pull together) while electric force can be attractive (opposite charges) or repulsive (same charges), and gravity depends on mass while electric force depends on charge. For macroscopic charged objects: For two 1 kg objects each with charge 1 μC = 10⁻⁶ C separated by 0.5 m, the gravitational force is F_grav = (6.67×10⁻¹¹)(1)(1)/(0.5)² ≈ 2.7 × 10⁻¹⁰ N (tiny), while the electric force is F_elec = (9.0×10⁹)(10⁻⁶)(10⁻⁶)/(0.5)² = 3.6 × $10^{-2}$ N (noticeable), a ratio of about $10^{11}$—even this modest laboratory charge produces electric forces that are a hundred billion times stronger than gravity between the same objects. Choice B is correct because it accurately identifies that electric force dominates at atomic scale due to the enormous force ratio of ~10¹¹ and properly applies both force formulas and compares the resulting magnitudes. Choice D has an error in the power of 10, reporting the ratio as $10^{-11}$ instead of the correct $10^{11}$, likely from incorrectly handling exponents when dividing powers of 10 in the calculation: (10⁹)/(10⁻¹¹) = 10²⁰ for the constants, combined with exponents from masses and charges. When comparing gravitational and electric forces: (1) both follow inverse square laws F ∝ 1/r², so distance affects them equally, (2) the ratio of strengths F_elec/F_grav = (kq₁q₂)/(Gm₁m₂) depends on charges and masses but not distance, (3) electric force is intrinsically stronger by a factor of k/G ≈ 10²⁰ when comparing equal numerical values, (4) at atomic scales electric dominates because particles have charge but tiny mass (gravity ≈ 10⁻⁴⁷ N is negligible), and (5) at cosmic scales gravity dominates because objects are massive but electrically neutral (equal + and - charges cancel, so net F_elec ≈ 0). Practical implications: chemistry, molecular biology, material strength, friction, and essentially all everyday phenomena (except falling) are determined by electric forces between atoms and molecules, while planetary orbits, tides, satellite motion, and the large-scale structure of the universe are determined by gravitational forces—the electric force's dominance at small scales is why a charged balloon can lift paper against Earth's entire gravitational pull, yet gravity's dominance at large scales is why planets orbit stars despite any residual electric charges they might have.

This question tests understanding of how gravitational and electric forces compare in magnitude and significance at different scales. Both gravitational force (F = Gm₁m₂/r²) and electric force (F = kq₁q₂/r²) follow inverse square laws, decreasing with the square of the distance between objects, but they differ dramatically in strength: the Coulomb constant k = 9.0 × 10⁹ N·m²/C² is about 10²⁰ times larger than the gravitational constant G = 6.67 × 10⁻¹¹ N·m²/kg², making electric forces intrinsically much stronger than gravitational forces for comparable numerical values. Additionally, gravity is always attractive (masses always pull together) while electric force can be attractive (opposite charges) or repulsive (same charges), and gravity depends on mass while electric force depends on charge. For scale dependence: The ratio F_elec/F_grav = (kq₁q₂)/(Gm₁m₂) is independent of distance r (since both forces have r² in denominator which cancels in the ratio), meaning the relative strength depends only on the charge-to-mass ratios of the objects—this is why electric forces dominate at atomic scales (where charge-to-mass ratio is high for particles like electrons) while gravity dominates at cosmic scales (where objects are electrically neutral with charge-to-mass ratio near zero, but masses are enormous). Choice B is correct because it correctly explains that gravity dominates at cosmic scale because massive objects are electrically neutral. Choice A suggests that the distance dependence is different for the two forces (claiming one decreases faster with distance than the other), when actually both follow inverse square laws (F ∝ 1/r²) and decrease at the same rate with distance—the ratio F_elec/F_grav = (kq₁q₂)/(Gm₁m₂) is independent of r. When comparing gravitational and electric forces: (1) both follow inverse square laws F ∝ 1/r², so distance affects them equally, (2) the ratio of strengths F_elec/F_grav = (kq₁q₂)/(Gm₁m₂) depends on charges and masses but not distance, (3) electric force is intrinsically stronger by a factor of k/G ≈ 10²⁰ when comparing equal numerical values, (4) at atomic scales electric dominates because particles have charge but tiny mass (gravity ≈ 10⁻⁴⁷ N is negligible), and (5) at cosmic scales gravity dominates because objects are massive but electrically neutral (equal + and - charges cancel, so net F_elec ≈ 0). The key insight is that electric force is far stronger intrinsically (k >> G by 10²⁰), yet gravity controls the cosmos—this apparent paradox resolves when you realize that charge comes in two types (+ and -) that cancel when combined, while mass comes in only one type (positive) that always adds up, so large objects like planets inevitably have huge total mass but near-zero net charge, making F_grav = G(M_planet)(M_star)/r² enormous while F_elec ≈ k(~0)(~0)/r² ≈ 0.

This question tests understanding of how gravitational and electric forces compare in magnitude and significance at different scales. Both gravitational force (F = Gm₁m₂/r²) and electric force (F = kq₁q₂/r²) follow inverse square laws, decreasing with the square of the distance between objects, but they differ dramatically in strength: the Coulomb constant k = 9.0 × 10⁹ N·m²/C² is about 10²⁰ times larger than the gravitational constant G = 6.67 × 10⁻¹¹ N·m²/kg², making electric forces intrinsically much stronger than gravitational forces for comparable numerical values. Additionally, gravity is always attractive (masses always pull together) while electric force can be attractive (opposite charges) or repulsive (same charges), and gravity depends on mass while electric force depends on charge. For a proton and electron separated by r = 1.0 × $10^{-10}$ m, the gravitational force is F_grav = G(m_p)(m_e)/r² ≈ $(6.67×10⁻¹¹)(1.67×10^{-27}$$)(9.11×10^{-31}$$)/(10^{-10}$)² ≈ 1.0 × $10^{-47}$ N, while the electric force is F_elec = $k(e)^2$ / r² = $(9.0×10⁹)(1.6×10^{-19}$$)^2$ / $(10^{-10}$)² ≈ 2.3 × $10^{-8}$ N, with ratio $~10^{39}$. Choice A is correct because it properly applies both force formulas and compares the resulting magnitudes. Choice C has an error in the power of 10, reporting F_elec as 2.3 × $10^{-28}$ instead of 2.3 × $10^{-8}$, likely from incorrectly handling exponents when dividing powers of 10 in the calculation: forgot the $r^2$ $=10^{-20}$ in denominator. When comparing gravitational and electric forces: (1) both follow inverse square laws F ∝ 1/r², so distance affects them equally, (2) the ratio of strengths F_elec/F_grav = (kq₁q₂)/(Gm₁m₂) depends on charges and masses but not distance, (3) electric force is intrinsically stronger by a factor of k/G ≈ 10²⁰ when comparing equal numerical values, (4) at atomic scales electric dominates because particles have charge but tiny mass (gravity ≈ 10⁻⁴⁷ N is negligible), and (5) at cosmic scales gravity dominates because objects are massive but electrically neutral (equal + and - charges cancel, so net F_elec ≈ 0). The key insight is that electric force is far stronger intrinsically (k >> G by 10²⁰), yet gravity controls the cosmos—this apparent paradox resolves when you realize that charge comes in two types (+ and -) that cancel when combined, while mass comes in only one type (positive) that always adds up, so large objects like planets inevitably have huge total mass but near-zero net charge, making F_grav = G(M_planet)(M_star)/r² enormous while F_elec ≈ k(~0)(~0)/r² ≈ 0.

This question tests understanding of how gravitational and electric forces compare in magnitude and significance at different scales. Both gravitational force (F = Gm₁m₂/r²) and electric force (F = kq₁q₂/r²) follow inverse square laws, decreasing with the square of the distance between objects, but they differ dramatically in strength: the Coulomb constant k = 9.0 × 10⁹ N·m²/C² is about 10²⁰ times larger than the gravitational constant G = 6.67 × 10⁻¹¹ N·m²/kg², making electric forces intrinsically much stronger than gravitational forces for comparable numerical values. At cosmic scales, gravity dominates not because electric force is weak, but because planets and stars have nearly equal amounts of positive and negative charge (electrically neutral), so net charge ≈ 0 makes F_elec ≈ 0 even though the intrinsic strength of electric force is much greater than gravity. Choice B is correct because it properly explains that planets and stars have enormous mass but near-zero net charge due to charge cancellation—matter contains equal numbers of protons and electrons, so large objects are electrically neutral despite containing vast amounts of charge. Choice A incorrectly suggests that electric forces decrease faster than gravity with distance, when actually both follow inverse square laws (F ∝ 1/r²) and decrease at the same rate with distance—the ratio F_elec/F_grav = (kq₁q₂)/(Gm₁m₂) is independent of r. The key insight is that electric force is far stronger intrinsically (k >> G by 10²⁰), yet gravity controls the cosmos—this apparent paradox resolves when you realize that charge comes in two types (+ and -) that cancel when combined, while mass comes in only one type (positive) that always adds up, so large objects like planets inevitably have huge total mass but near-zero net charge, making F_grav = G(M_planet)(M_star)/r² enormous while F_elec ≈ k(~0)(~0)/r² ≈ 0.

This question tests understanding of how gravitational and electric forces compare in magnitude for macroscopic charged objects with different masses and charges. Both gravitational force (F = Gm₁m₂/r²) and electric force (F = k|q₁q₂|/r²) follow inverse square laws, decreasing with the square of the distance between objects, but they differ dramatically in strength: the Coulomb constant k = 9.0 × 10⁹ N·m²/C² is about 10²⁰ times larger than the gravitational constant G = 6.67 × 10⁻¹¹ N·m²/kg², making electric forces intrinsically much stronger than gravitational forces for comparable numerical values; additionally, gravity is always attractive while electric force can be attractive or repulsive, and gravity depends on mass while electric force depends on charge. For the given spheres separated by 0.20 m, F_grav ≈ 6.7 × 10⁻¹⁰ N and F_elec ≈ 0.90 N, showing electric force is much larger. Choice A is correct because it properly calculates the magnitudes using both force formulas and reports them accurately. Choice B inverts the magnitudes, incorrectly assigning the larger value to gravity when actually electric force is vastly stronger due to the charges involved. When comparing gravitational and electric forces: (1) both follow inverse square laws F ∝ 1/r², so distance affects them equally, (2) the ratio of strengths F_elec/F_grav = (kq₁q₂)/(Gm₁m₂) depends on charges and masses but not distance, (3) electric force is intrinsically stronger by a factor of k/G ≈ 10²⁰ when comparing equal numerical values, (4) at atomic scales electric dominates because particles have charge but tiny mass (gravity ≈ 10⁻⁴⁷ N is negligible), and (5) at cosmic scales gravity dominates because objects are massive but electrically neutral (equal + and - charges cancel, so net F_elec ≈ 0). The key insight is that electric force is far stronger intrinsically (k >> G by 10²⁰), yet gravity controls the cosmos—this apparent paradox resolves when you realize that charge comes in two types (+ and -) that cancel when combined, while mass comes in only one type (positive) that always adds up, so large objects like planets inevitably have huge total mass but near-zero net charge, making F_grav enormous while F_elec ≈ 0.