Determine the decrease in the weight of a body when it is taken 32 km below the earth surface. Take radius of the earth as 6400 km.

Options

A. `1%`
B. `2%`
C. `1.5%`
D. `5%`

Answer

A

Explanation

In this case, `h lt lt R " " therefore g_(h)=g(1-(2h)/(R ))=g-(2gh)/(R )`
`therefore g-g_(h)=(2gh)/(R )" "` ……..(1)
`therefore` Percentage decrease in weight
`= (mg-mg_(h))/(mg)xx100`
`=((g-g_(h))/(g))xx100=(2gh)/(gR)xx100 " "` ......from (1)
`=(2h)/(R )xx100=(2xx32)/(6400)xx100=1%`
`therefore` Percentage decrease = 1%