NDA (I) 2018 General Ability Test · Question 58 of 150

Correct — D, It is same for all pairs of bodies in our universe. Newton's law of gravitation says the force between two bodies is the gravitational constant times the product of their masses divided by the square of the distance between them. Only the constant G is the same everywhere; the force itself changes the moment either mass or the separation changes. The Sun pulls the Earth with a force of about 3·5 × 10²² newtons, while two people standing a metre apart attract each other with a force far too small to feel. Saying the force is the same for all pairs confuses the universal constant with the force, so this is the statement that is not correct.

• (a)It is experienced by all bodies in the universe — Correct, and it is the reason the law is called universal. Every body with mass attracts every other body with mass, which is exactly what Newton claimed in extending the falling apple to the orbiting Moon.
• (b)It is a dominant force between celestial bodies — Correct. Stars, planets and galaxies are electrically neutral overall, so the far stronger electromagnetic force cancels out over large bodies, and the nuclear forces reach only across a nucleus. Gravity, which never cancels because there is no negative mass, is left in charge.
• (c)It is a negligible force for atoms — Correct. Between two protons the electrostatic repulsion is stronger than their gravitational attraction by a factor of about ten to the power thirty-six, so gravity plays no part in atomic structure.

Newton's universal law of gravitation states that every particle attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. The constant of proportionality G is about 6·67 × 10⁻¹¹ newton metre squared per kilogram squared, and it is the same throughout the universe. Gravitation is the weakest of the four fundamental interactions but the only one that is always attractive and unlimited in range, which is why it governs the large-scale structure of the cosmos.

The item hinges on one word — 'same'. Something in gravitation genuinely is the same everywhere, and that is G, the universal gravitational constant; that is what makes the law universal. The force is not. Reading option (d) carefully shows it has swapped the constant for the force. A second useful check is to notice how well the other three options hang together. Gravity being negligible for atoms and dominant for planets are two sides of one fact: gravity is extremely weak per unit mass but it never cancels, so it wins whenever the masses get large enough. Bear in mind too that the inverse-square dependence means the force falls to a quarter when the separation doubles, which is the calculation NDA sets most often.

• The gravitational force between two masses varies as the product of the masses and inversely as the square of the distance between them.
• The gravitational constant G is about 6·67 × 10⁻¹¹ N m² kg⁻² and has the same value everywhere.
• Gravitation is the weakest of the four fundamental forces but has unlimited range and is always attractive.
• It is a non-contact force, acting across empty space without the bodies touching.
• Doubling the separation reduces the force to one-quarter of its value.

• Confusing the universal constant G with the acceleration due to gravity g.
• Assuming gravitation is strong because it holds planets in orbit; it is the weakest of the four forces and wins only because it never cancels.
• Forgetting that the force is inverse-square, not inversely proportional to distance.

Either as a statement-screening item like this one, or numerically by scaling the masses and the separation together and asking for the new force.

• practice — not a real PYQ

  If the distance between two bodies is tripled, the gravitational force between them becomes

  • (a)three times
  • (b)one-third
  • (c)one-sixth
  • (d)one-ninth

  Answer(d) one-ninth — the force varies inversely as the square of the distance, and three squared is nine.

• practice — not a real PYQ

  Which of the following is the same everywhere in the universe?

  • (a)The acceleration due to gravity g
  • (b)The gravitational force between two bodies
  • (c)The universal gravitational constant G
  • (d)The weight of a one-kilogram mass

  Answer(c) The universal gravitational constant G — g, the force and the weight all change with circumstances, but G does not.