Question

prove that intensity of gravitational field is directly proportional to acceleration due to gravity​

Answer 1

Answer:

Gravitational Field Intensity is a vector quantity denoting the force acting on a unit mass at a point in the gravitational field.

$\huge\green{f = G \frac{m1m2}{ {r}^{2} }}$

Now, for a unit mass at a particular point from the reference ,

$\huge{ \green{intensity = \frac{Gm2}{ {r}^{2} } }}$

Now for any planet , let's consider a mass m1 being pulled by a planet m2 , we get :

$\huge\green{force = G \frac{m1m2}{ {r}^{2} }}$

Now gravitational acceleration = F/(m1)

$\huge{ \green{g = \frac{Gm2}{ {r}^{2} } }}$

So we see that gravitational intensity and gravitational acceleration is same.

Answer 2

Answer:

Gravitational Field intensity is numerically equal to the force experienced on a unit mass placed in a field with respect to a reference mass.

Let the reference mass be m, and force be F.

$\boxed{ | \vec{F}| = \dfrac{Gm1 \times 1}{ {r}^{2} }}$

Now since we are considering unit mass, we can call this force equivalent to field intensity :

Let field intensity be denoted by E

$\boxed{ \red{ | \vec{E}| = \dfrac{Gm1}{ {r}^{2} }}}$

Now , gravitational acceleration :

$\boxed{force =G \dfrac{m1 \times m2}{ {r}^{2} }}$

$\boxed{\red{ \therefore{acc. = g = \frac{force}{mass } = G \frac{m1}{ {r}^{2} }}}}$

So we can see that gravitational acceleration is actually equal to gravitational Field intensity.