Question

If both the mass and the radius of the earth decrease by 1%, then the value of acceleration due to gravity will

Options

• decrease by 1%.

• increase by 1%.

• increase by 2%.

• remain unchanged.

Answer 1

increase by 1%.

Explanation:

The gravitational acceleration is given by g = `(GM)/R^2`

If both M and R are reduced by 1%, their values become 0.99 Mand 0.99 R, and the acceleration due to gravity becomes,

g' = `(GM)/(R)^2 (G xx 0.99  M)/(0.99  R)^2 = 1.01 xx (GM)/R^2` = 1.01 g

∴ `g^' - g = 1.01 g - g` = 0.01 g

∴ `(g^' - g)/g xx 100` = 1%