UPSC Prelims 2003·GS1·science-and-technology·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

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Last updated 8 Jul 2026, 4:39 pm IST
  1. Aincrease by 0.5%
  2. Bincrease by 2%Correct
  3. Cdecrease by 0.5%
  4. Ddecrease by 2%

Explanation

The value of acceleration due to gravity g is calculated using the formula g equals G times M divided by R squared, where G is the gravitational constant, M is the mass of the earth, and R is its radius.

Since the mass M remains constant, g is inversely proportional to the square of the radius R. In physics, for small percentage changes, the percentage change in g is approximately equal to minus two times the percentage change in R.

If the radius R shrinks by 1 percent, the change is negative 1 percent. Multiplying this by negative 2 results in a positive 2 percent. Therefore, the value of g increases by 2 percent. This happens because as the surface moves closer to the center of mass while the mass stays the same, the gravitational pull becomes stronger.

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 sur
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