What will be the value of acceleration due to gravity on the surface of the earth if the radius of the earth suddenly decreases to 60% of its present value, keeping the mass of the earth unchanged?
(a) 9.81 m/s^2
(b) 5.89 m/s^2
(c) 16.35 m/s^2
(d) 27.25 m/s^2
This question was addressed to me in my homework.
My question is from Universal Law of Gravitation in portion Gravitation of Physics – Class 11
Select the correct answer from above options
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The correct option is (d) 27.25 m/s^2
For explanation I would say: From Newton’s law of gravitation, we have;
g = (G*M1)/R^2
Since the radius is reduced to 60% of its original value;
The new radius R’ = 0.6 x R
g’ = (G*M1)/(0.6*R) ^2
g’ = g/(0.6) ^2
= 9.81 / (0.6 x 0.6)
g’ = 27.25 m/s^2.