Question

at what altitude from earth's surface will the acceleration due to gravity be 25%as that on the earth's surface (Given that the radius of earth is R) option a. R/4 b. 3R/8 c. R d. R/2​

Answer 1

Answer:

c.R

Explanation:

Force on the body placed on Earth's surface is

$F= \frac{GMm}{R^{2} }$

But, F=mg hence,

mg= $\frac{GMm}{R^{2} }$

where, variables have their usual meanings.

g$R^{2}$= GM

Now, force on the body at geo-potential  height say h (altitude) where the acceleration due to gravity is 25% of that at the earth's surface i.e.

$\frac{25g}{100}$$=\frac{g}{4}$

Hence, we can write

$\frac{g}{4} =\frac{GM}{(R+h)^{2} }$

$(R+h)^{2} = 4R^{2}$

Taking roots for both sides we get

R+h=2R

h=R

Answer 2

Answer:

Force on the body placed on Earth's surface is

But, F=mg hence,

mg=  

where, variables have their usual meanings.

g= GM

Now, force on the body at geo-potential  height say h (altitude) where the acceleration due to gravity is 25% of that at the earth's surface i.e.

Hence, we can write

Taking roots for both sides we get

R+h=2R

h=R

Explanation: