If the value of the universal gravitation constant (G) was accidentally used as ten times higher in a planetary orbit calculation, what would be the effect on the calculated gravitational force between the planet and the sun?

Appeared in: RRB Nsg. Superintendent-2026 (Shift -2nd)

Explanation

Newton's Law of Universal Gravitation is expressed by the formula F = G × (m₁m₂/d²), where F is the gravitational force and G is the universal gravitational constant.
The formula shows that the force (F) is directly proportional to the gravitational constant (G). This means if G changes, F changes by the exact same factor, assuming mass and distance are constant.
If the value of G used in the calculation is multiplied by 10, the resulting force F will also be multiplied by 10, making the calculated force ten times greater than the actual force.

Option A: This option suggests an inverse relationship where multiplying G by 10 would decrease F. The relationship is direct, not inverse.
Option C: A result of half the actual value would require the constant G to be halved (i.e., multiplied by 0.5), not multiplied by 10.
Option D: This is incorrect because G is a direct and essential multiplier in the gravitational force equation. Any change in G must result in a change in F.

Visual 1: Diagram - An infographic illustrating Newton's Law of Universal Gravitation, showing two masses (like the sun and a planet), the distance 'd' between them, and the force vector 'F'. The formula F = G * (m1*m2)/d^2 should be prominently displayed.
Visual 2: Graph - A simple linear graph showing Force (F) on the y-axis and the Gravitational Constant (G) on the x-axis. The graph would be a straight line passing through the origin, visually representing the direct proportionality between F and G.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Newton's Law of Universal Gravitation and the concept of direct proportionality in physics formulas as background academic context rather than a clinical decision trigger.
Although this is a physics question, the underlying principle of precision with constants is paramount in nursing. Dosage calculations rely on correct formulas and conversion factors (which are a type of constant).
An error in a constant, such as a drug concentration or a conversion factor (e.g., lbs to kg), can lead to a significant medication error, potentially causing severe harm to a patient.
This principle of direct proportionality is also seen in medicine. For example, within a certain range, increasing the infusion rate of a drug (like a vasopressor) leads to a proportional increase in its physiological effect (like blood pressure).

How to Approach the Question

Step 1: Identify the core scientific principle being tested. Here, it is Newton's Law of Universal Gravitation.
Step 2: Recall or write down the mathematical formula associated with the principle: F = G × (m₁m₂/d²).
Step 3: Analyze the relationship between the variables mentioned in the question. The question asks about the effect of changing the constant G on the force F.
Step 4: Observe from the formula that F is directly proportional to G. This means F = k × G, where k is (m₁m₂/d²).
Step 5: Apply the specific change given in the problem. The value of G is used as '10 × G'. Substitute this into the relationship: F' = k × (10 × G) = 10 × (k × G) = 10 × F.
Step 6: Conclude that the new calculated force (F') is ten times the original force (F) and select the matching option.

Concept Tested & Keywords

Concept Tested: Newton's Law of Universal Gravitation and the concept of direct proportionality in physics formulas.
Stem keywords: universal gravitation constant (G), gravitational force, planetary orbit calculation
Lead-in keywords: what would be the effect
Negative lead-in flag: false

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Practise the full RRB Nsg. Superintendent-2026 (Shift -2nd)

Attempt every question from this paper in a timed mock, then review the full solution for each one.