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

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Q: 79 (IAS/2003)
If the radius of the earth were shrink by one per cent , its mass remaining the same, the value of ‘g’ on the earth’s surface would

question_subject: 

Science

question_exam: 

IAS

stats: 

0,28,56,24,28,18,14

keywords: 

{'radius': [0, 0, 2, 2], 'earth': [0, 1, 1, 1], 'per cent': [0, 1, 0, 0], 'mass': [0, 0, 2, 3]}

The value of `g` or acceleration due to gravity on the earth`s surface can be calculated using the formula g = GM/r^2, where G is the gravitational constant, M is the mass of the earth, and r is the radius of the earth.

Option 1 and 3 suggest decreasing values for `g`, which is not possible, as the mass `M` remains the same, but the radius `r` is decreasing, which should increase the value of `g` (as they are inversely proportional).

Option 2 suggests that `g` will increase by 2%. This is because the formula is inversely related to the square of the radius. So, if you decrease the radius by 1%, the effect on `g` will be roughly double that.

Option 4 suggests a decrease of 2% which contradicts the inverse relationship in the formula.

Remember, only an approximate value is considered in this question. The actual value might differ due to external factors not considered here.