The acceleration due to gravity at a depth d below the surface of the earth is 20% of its value at the surface. What is the value of d if the radius of the earth=6400km ?

Options

A. 5120km
B. 4600km
C. 7350km
D. 2840km

Answer

A

Explanation

`because g_(d)=g(1-(d)/(R ))" " therefore (g_(d))/(g)=(1-(d)/(R ))`
`(20)/(100)=(1)/(5)=1-(d)/(R )`
`therefore (d)/(R )=1-(1)/(5)=(4)/(5)`
`therefore d=(4)/(5)R=(4)/(5)xx6400 =5120 km`