Question

Calculate the height above the Earth's surface at which the value of acceleration due to scravity reduces to half its value on the Earth's surface. Assume the Earth to be a sphere of radius 6400 km.​

Answer 1

Answer:

2650

Explanation:

The new value of gravity at a height h is given as g′=

(R+h)

2

gR

2

As visible from the formula that incresing h results in decresing gravity.

So just put g′=g/2 i.e. 50% less than g where g is gravity at surface. so we get g/2=

(R+h)

2

gR

2

or

2

1

=

(R+h)

2

R

2

or

1

2

=

R

2

(R+h)

2

or

2

2

=

R

R+h

=1+h/R putting values we get

R

h

=1.414−1=0.414

so h=0.414R=2649.6Km