if the radius of earth shrinks by 1% without change in its mass what will be the increase in g at its surface
Dear Aman, the acceleration due to gravity will increase by 2%.
g=GMR^-2
On differentiating,
dg/dr= -2× g/R
Negative sign accounts for the decrease in the radius.
Now substituting dr as -1, we get dg = 2 times a quantity.
Thus accelerationddue to gravity increases by 2%.
All the best
Hope this helps
Hello there!
Greetings!
If acceleration due to gravity on earth(g) = G.M/R²,
then weight of the body = mg;
where G is gravitation constant, M is mass of earth and R is the radius.
Now if the radius is reduced by half it means g is reduces by 1/4th because it is inversely proportional to the square of radius.
And weight of the body is directly proportional to g, it will also reduce by a factor of 4.
Thankyou
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