Question

find the height at which change in acc due to gravity is 30%.

Answer 1

We know that gravity at any height is given as;

g’ = g (1 - 2h/R) —[1]

Decrease by 1% implies that g’ = 99/100g

Substitute In 1,we get

99/100g = g (1 - 2h/R)

99/100 = 1 - 2h/R

2h/R = 1 - 99/100

2h/R = 1/100

h = R/200

h = 6400/200 (R = 6400KM)

H = 32KM From surface of earth

Answer 2

Explanation:

The height of mercury in barometer increases by 3%, if the acceleration due to gravity decreased by 30%

Explanation:

The pressure in the mercury barometer is defined by the formula,

P=\rho h g \rightarrow(1)

So,

h=\frac{P}{\rho g} \rightarrow(2)

Where,

P is the pressure in the barometer

ρ is mercury’s density

g is the acceleration due to gravity

The term P/ρ will remain constant in barometer. So it states that height of mercury will be inversely proportional to the acceleration due to gravity.

The change in height of the mercury in barometer can be found by differentiating eqn (2), we get,

\Delta h=\frac{P \Delta g}{\rho g^{2}} \rightarrow(3)

Now, divide eqn (3) with eqn (2)

\frac{\Delta h}{h}=-\frac{P \Delta g}{\rho g^{2}} \times \frac{\rho g}{P}

So,

\frac{\Delta h}{h}=-\frac{\Delta g}{g} \rightarrow(4)

As it is given in question,

\Delta \frac{g}{g}=-30 \%

On substituting this in eqn (4), we get,

\frac{\Delta h}{h}=3 ,0\% \rightarrow(5)

So the height of the mercury in barometer increases by 30%