What would be the magnitude of the acceleration due to gravity on the surface of the earth if the radius of the earth were reduced by 20%?

Category: QuestionsWhat would be the magnitude of the acceleration due to gravity on the surface of the earth if the radius of the earth were reduced by 20%?
Editor">Editor Staff asked 1 year ago

What would be the magnitude of the acceleration due to gravity on the surface of the earth if the radius of the earth were reduced by 20%?
 
(a) 9.81 m/s^2
 
(b) 12.26 m/s^2
 
(c) 15.33 m/s^2
 
(d) 49.05 m/s^2
 
The question was posed to me by my school principal while I was bunking the class.
 
My question comes from Acceleration due to Gravity of the Earth topic in division Gravitation of Physics – Class 11
Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 1 year ago

Correct answer is (c) 15.33 m/s^2
 
Easy explanation: g = (G*M1)/R^2;
 
M1 = Mass of the earth
 
R = Radius of the earth
 
We know; g = 9.81 m/s^2
 
If the radius is reduced by 20% then the new radius is 80% of the original one;
 
New radius = 0.8R
 
Therefore, new acceleration;
 
g / (0.8 x 0.8) = 9.81 / 0.64
 
= 15.33 m/s^2.


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