Question

The value of acceleration due to gravity 'g' varies with the​

Answer 1

Answer:

varies with height of the object which means when we are on the earth surface the g=9.8m/s^2 it usually uses while calculating

Answer 2

To FinD :-

• The value of acceleration due to gravity 'g' varies with ?

SolutioN :-

Acceleration due to gravity is the acceleration produced due to the force of attraction by the Earth . It is denoted by g . It's approximate value is 9.8 m/s² ≈ 10 m/s² .

Let us take ,

$\red{\frak{ Let}}\begin{cases}\textsf{ Mass of the earth be M .}\\\textsf{ Mass of object be m .}\\\textsf{ Distance between them be r .}\end{cases}$

Now we know that the Force of attraction is directly proportional to the product of masses of the bodies and inversely proportional to the square of distance between them. That is ,

$\sf:\to F = G \dfrac{Mm}{r^2}$

And here the force is in the form of weight that is mg . So that ,

$\sf:\implies \pink{ F = G \dfrac{Mm}{r^2}}\\\\\sf:\implies mg=G \dfrac{Mm}{r^2} \\\\\sf:\implies g = \dfrac{GM}{r^2}$

Now here G is Constant . So , using sign of Proportionality , we have ,

$\sf\dashrightarrow \pink{ g \propto \dfrac{M}{r^2}}$

Therefore , we see that g is directly proportional to the mass of the planet . And inversely proportional to the square of distance .