Question

if the radius of a Planet shrinks by 2% while its mass remains the unchanged the acceleration due to gravity on the planet surface would increase or decrease?

Answer 1

planet surface would increase because

The acceleration due to gravity at the surface of earth is g = G m / R2  .

The radius of earth decreases by 2 %, therefore

R' = R - 0.02 R = 0.98R.

Now acceleration due to gravity will be :

g' = GM / ( 0.98 R )2  = 1.04 g

Percentage increase in acceleration due to gravity

[(g' - g )/g ] x 100 = 4 %

i hope this clarifies your doubt.

Regards

Answer 2

Hola User__________________

Here is Your Answer..!!!!
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⭐Actually welcome to the concept of the GRAVITATION...

⭐Now Basiclly we know that ......

⭐F = GMm/r^2 ...

⭐since we know that .. F = mg ( for a body at surface )

⭐thus we get that ....

⭐g = GM / r^2

⭐Now from this expression we can clearly see that the .... Acceleration due to gravity is always inversely proportional to the Radius of the planets ...

⭐so now we can say that. ..when the Radius decreases the Acceleration due to gravity (g) will increase as they are in inverse proportion to each other

⭐So the value of Acceleration due to the gravity increases

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Hope it helps u.....☺