Question

If the radius of the earth decreases by of mass being constant then the acceleration due to gravity
a) Decreases by 19%
b) Increases by 19%
c) Decreases by more than 19%
d) Increases by more than 19%
plz answer fast​

Answer 1

i think it's d

i am not sure sis

Answer 2

The complete question is:

If the radius of the earth decreases by 10%, mass being constant then the acceleration due to gravity

:

a) Decreases by 19%

b) Increases by 19%

c) Decreases by more than 19%

d) Increases by more than 19%

Given:

Percentage decrease in radius = 10%

To find:

The correct option.

Solution:

Let the radius of the Earth be R, when radius decreases by 10%, then:

Radius R'= R - 10R/100

R' = R - 0.1R

R' = 0.9R

We know that acceleration due to gravity g = GM/ R²

When radius decreases,

g' = GM/ (0.9R)²

g' = GM/ 0.81R²

g' = g/ 0.81

Increase in acceleration due to gravity Δg = g' - g

= g/0.81 - g  = 0.19g/ 0.81

Percentage increase = Δg/g *100

=(0.19g/ 0.81g) * 100

= 23.45%

The correct option is (d) which is: Increases by more than 19%.