Question

The value of 'g' reduces to half of its value at surface
of earth at a height 'h', then :-
(1) h-R
(2) h = 2R
(3) h= (2+1)R
(4) h= (2-1)R​

Answer 1

Answer:

Given:

Value of "g" reduces to half it's value as that of the surface of the Earth .

To find:

The height at which such variation occurs.

Concept:

With increase in height, the Gravitational force decreases. It can be mathematically formulated as

g" = g/(1+h/R)²,

h ------> height above the earth surface.

R ------> Radius of the Earth

g ------> initial gravity

g" -----> New gravity

Calculation:

As per the question : g" = g/2

So,

g/2 = g/(1+h/R)²

=> ½ = 1/(1 + h/R)²

=> 2 = (1 + h/R)²

=> √2 = 1 + h/R

=> h/R = √2 - 1

=> h = (√2 - 1 ) R.

Answer 2

Question:-

The value of 'g' reduces to half of its value at surface

of earth at a height 'h', then :-

$\huge\sf{\underline{\underline{Solution:}}}$

▪Given that:-

• The value of 'g' reduces to half of its value at surface of earth at a height 'h'.

▪To find:-

• The height.

______________________________

$\implies$g/2 = g/(1+h/R)²

1/2= 1/(1 + h/R)^2

2 = (1 + h/R)^2

√2 = 1 + h/R

h/R = √2 - 1

h = (√2 - 1 ) R.

Hence, D) option is correct