Question

the value of g at a particular point is 9.8 metre per second square . suppose the earth suddenly shrinks uniformly to half its present size without losing any mass what is the value of g at the same point?

Answer 1

The value of g at the same point will be equal to :-

$4 \times 9.8 = 39.2 \: m \: per {sec}^{2}$



Please refer the above photograph for the used process.


KEY POINTS TO REMEMBER :-


☸️ 'g' refers to the acceleration due to gravity which acts on everything present on the earth.
This is rate at which the earth attracts an object.


☸️ The equation for finding g is :-

$g = \frac{capital \: g \: \times m}{ {r}^{2} }$

Where
g is the acceleration due to gravity, capital g or G is the gravitation constant,. M is the mass of the planet and R is the radius of the planet.


How did it came??


It is said in Kepler's laws of Planetary motion :-that acceleration due to gravity is directly proportional to mass of the planet and inversely proportional to the square of the radius of the planet.


This means that :-

g is directly proportional to M

And,
g is inversely proportional to R²

So,

Mathematically if we express we get :-

$g \: is \: proprtional \: to \: \frac{m}{ {r}^{2} }$


To remove the proportionality sign we multiply a constant.
In this case it is the Gravitation constant known as G.

So,


$g = \frac{capital \: g \times m}{ {r}^{2} }$



Thanks!

Answer 2

Answer:

Explanation . Look bellow