2003 General Studies, all questions
UPSC Prelims 2003 · General Studies
Question 79: Science and Technology
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
aincrease by 0.5%
bincrease by 2%
cdecrease by 0.5%
ddecrease by 2%
AnswerThe answer is (b).
Surface gravity g = GM/R squared. With the mass M constant, g varies inversely as the square of the radius. A 1 per cent decrease in R multiplies g by 1/(0.99)^2, which is about 1.0203, an increase of nearly 2 per cent. For small changes, a fall of x per cent in R raises g by about 2x per cent.
Why each option is right or wrong
- (a) 0.5 per cent ignores that g depends on R squared.
- (b) Correct: g rises by about 2 per cent.
- (c) g rises when the radius shrinks; it does not fall.
- (d) g rises, not falls, when the radius shrinks.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2003, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.