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BITSAT 2012
Exam
BITSAT
Year
2012
Subject
Physics
Chapter
Gravitation

BITSAT 2012 · Physics · Gravitation

If the radius of the earth were to shrink by one per cent, its mass...

If the radius of the earth were to shrink by one per cent, its mass remaining the same, the value of g on the earth's surface would

Options

  1. Aincrease by 0.5%0.5 \%
  2. Bincrease by 2%2 \%
  3. Cdecrease by 0.5%0.5 \%
  4. Ddecrease by 2%2 \%

Correct answer

B. increase by 2%2 \%

Step-by-step solution

g=GMR2⇒dgg=−2dRRdRR=−1%⇒dgg=2%\quad \mathrm{g}=\frac{\mathrm{GM}}{\mathrm{R}^{2}} \Rightarrow \frac{\mathrm{dg}}{\mathrm{g}}=-2 \frac{\mathrm{dR}}{\mathrm{R}}\frac{\mathrm{dR}}{\mathrm{R}}=-1 \% \Rightarrow \frac{\mathrm{dg}}{\mathrm{g}}=2 \%
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