Acceleration due to gravity on the surface of the earth is `g = (GM)/(R^(2))`. The gravitational constant G is exacity known. But percentage error in measurement of the mass of earth `M` and radius of the earth `R` are `1%` and `2%`, respectively. The maximum percentage error in measurement of acceleration due to gravity on the surface of the earth is

Options

A. `2%`
B. `5%`
C. `3%`
D. `7%`

Answer

b

Explanation

`:' g = (GM)/(R^(2))`
`:. (Delta g)/(g) = (Delta M)/(M)+ (2Delta R)/(R)`
Percentage error in g is
`(Delta g)/(g)xx 100 = (Delta M)/(M)xx 100 + (2Delta R)/(R )xx 100`
` = 1 + 4 = 5%`