Question

Q.3. Derive the formula to calculate the value of ‘g’.​

Answer 1

The acceleration produced in freely falling body due to gravitational force is called acceleration due to gravity.

 

Acceleration due to gravity is represented by letter 'g'.

 

Value of g is 9.8 m/s2 . 

 

Derivation of acceleration due to gravity: 

 

As per Newton's law, Force = mass × acceleration = m×a .....................(1)

 

where m is mass and a is acceleration

 

Gravitational force acting on a mass m on earth's surface =  ..........................(2)

where G is Gravitational force constant, M is mass of earth and R is radius of earth

 

By comparing (1) and (2), acceleration due to gravity = g = (G×M)/R2

 

Answer 2

HELLO DEAR,

GIVEN:- Derive the the formula to calculate the value of 'g'.

SOLUTION:- Before deriving the formula of 'g' ,lets know what is 'g'.

'g' is a acceleration produce by earth gravitational force on any body which have mass.

From the Newton's law of motion, if you want to accelerate any body then we have to apply some force at the direction you want acceleration.

Therefore , Newtown introduce a formula ,which is the relation of mass and acceleration is called Newton's third law of motion.

F = ma. ( F= force applied on object)

( m = mass of object. )

( a = acceleration. )

As we know that gravitational force between two bodies,

F = (G Mm) / r^2............(i)

where M = mass of earth

m = mass of any object

r= distance between two

mass.

And F = ma. ( a= acceleration due to some external force)

Or F = mg. ............(ii)

( g= acceleration due to gravitational force)

By comparing equation (i) and (ii) ,we get

mg =( GMm) / r^2

g = (GM) / r^2

And the value of g is obtain by putting the value of G ( Universal gravitational constant) , M ( mass of earth) and 'r' ( distance above the earth surface) in above equation ,

and we get the value of

g = 9.8 m/ s^2.

I HOPE IT'S HELP YOU DEAR,

THANKS.