Question

9. Calculate the value of the acceleration due to gravity
at a place 3,200 km above the surface of the earth.

Answer 1

Given data : Place above the earth surface at height 3200 km.

To find : The value of the acceleration due to gravity at a place 3,200 km above the surface of the earth.

Solution : Here, we knohw that,

⟹ 3200 km = 3200000 m

⟹ 3200 km = 32 * 10^( 5 ) m

Now, we use formula : to calculate the value of the acceleration due to gravity,

⟹ gh = g { R/ R + h }²

Where,

• gh = acceleration due to gravity at height h
• g = acceleration due to gravity ( 9.8 m/s² )
• R = radius of earth ( 6400 km )
• h = height above earth surface

Here,

⟹ 6400 km = 6400000 m

⟹ 6400 km = 64 * 10^( 5 ) m

Now, by formula :

⟹ gh = g { R/ R + h }²

⟹ gh = 9.8 { 64 * 10^( 5 )/ 64 * 10^( 5 ) + 32 * 10^( 5 ) }²

⟹ gh = 9.8 { 64 * 10^( 5 )/ 96 * 10^( 5 ) }²

⟹ gh = 9.8 { 64/96 }²

⟹ gh = 9.8 { 3/2 }²

⟹ gh = 9.8 * 9/4

⟹ gh = 88.2/4

⟹ gh = 22.05 m/s²

Answer : Hence, the acceleration due to gravity at a place 3,200 km above the surface of the earth is 22.05 m/s².