Question

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

Answer 1

To find : The value of the acceleration due to

gravity at a place 3,200 km above the surface of the eearth ?

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 { 2/3 }²

⟹ gh = 9.8 * 4/9

⟹ gh = 39.2/9

⟹ gh = 4.35 m/s² (approx)

Answer : Hence, the acceleration due to gravity at a place 3,200 km above the surface of the earth is 4.35 m/s².