Question

23- If the radius of the earth were to decreases by 1%, keeping its mass same, how will the
acceleration due to gravity hange?​

Answer 1

ANSWER:

• The change in acceleration due to gravity = 0.02 g.

GIVEN:

• The radius of the earth decreased by 1 %, keeping its mass same.

TO FIND:

• The change in acceleration due to gravity.

EXPLANATION:

$\bigstar\ \boxed{\bold{\large{\blue{g =\dfrac{GM}{r^2}}}}}$

G is the Universal gravitational constant so it will not change.

Given that mass is kept fixed.

So radius alone will infuence the change in acceleration due to gravity.

$\sf \dashrightarrow\dfrac{\Delta g}{g} \times 100 \ \%=2\dfrac{\Delta r}{r}\times 100 \ \%$

$\sf \dashrightarrow\dfrac{\Delta r}{r}\times 100 \ \% = 1 \ \%$

$\sf \dashrightarrow\dfrac{\Delta g}{g} \times 100 \ \%=2( 1 \ \%)$

$\sf \dashrightarrow\dfrac{\Delta g}{g} \times 100 \ \%=2 \ \%$

$\sf \dashrightarrow\Delta g = 2 \ \% \ of \ g$

$\sf \dashrightarrow\Delta g =0.0 2g$

Hence acceleration due to gravity will become g + 0.02 g.