If the radius of earth shrinks by 2 % while its mass remains same. The acceleration due to gravity on the earth's surface will approximately :

Question

If the radius of earth shrinks by 2 % while its mass remains same. The acceleration due to gravity on the earth's surface will approximately : (A) decrease by 2 % (B) decrease by 4 %  (C)  increase by 2 % (D) increase by 4 %

Tardigrade Admin · Accepted Answer

g =( GM / R 2) M = text constant g <(1/ R 2) 100 (Δ g / g )=-2 (Δ R / R ) 100 % change =-2(-2) % change in g =4 % increase by 4 %

Q. If the radius of earth shrinks by $2%$ while its mass remains same. The acceleration due to gravity on the earth's surface will approximately :

decrease by $2%$

decrease by $4%$ $

$in cre a se b y$ 2 \%$

increase by $4%$

$g = \frac{GM}{R ^{2}}$
$M = constant g < \frac{1}{R ^{2}}$
$100 \frac{Δ g}{g} = - 2 \frac{Δ R}{R} 100$
$%$ change $= - 2 (- 2)$
$%$ change in $g = 4%$
increase by $4%$

Q. If the radius of earth shrinks by 2% while its mass remains same. The acceleration due to gravity on the earth's surface will approximately :

decrease by 2%

decrease by 4% $

increaseby2 \%$

increase by 4%