UPSC Prelims 2003 Q79: Science & Technology – Physics
If the radius of the earth were shrunk by one per cent, its mass remaining the same, the
value of ‘g’ on the earth’s surface would
- (a) increase by 0.5%
- (b) increase by 2%
- (c) decrease by 0.5%
- (d) decrease by 2%
Answer: (b) increase by 2%
Explanation
Effect of shrinking the earth's radius on g
| Quantity | Result |
|---|---|
| Formula | g = GM / R^2, so g varies inversely as R^2 |
| Radius decreases by 1% | R becomes 0.99 R |
| g changes by | 1/(0.99)^2 = 1.0203, an increase of about 2% |
Since g is proportional to 1/R^2, a 1 percent decrease in the radius with the same mass increases g by about 2 percent.
Answer: (b) increase by 2%.
Why each option is right or wrong
- (a) Incorrect. 0.5% would be for a change in R by 0.25%.
- (b) CORRECT. g changes by about twice the percentage change in R, in the opposite sense.
- (c) Incorrect. g increases, not decreases.
- (d) Incorrect. g increases, not decreases.
Key point
Small change: delta g / g = -2 delta R / R.
Remember
If R falls by 1% with M fixed, g rises by about 2%.
Common mistakes
- Taking the change in g as just 1%, not 2%.
- Choosing a decrease because the earth shrinks.
- Forgetting the square in the denominator.
Exam tip
Power law: percentage change is the power times the percentage change in the variable.
Sources
- NCERT Class XI Physics — Gravitation
- H. C. Verma — Concepts of Physics, Volume 1 (Gravitation)