Question

A body of mass `100kg` falls on the earth from infinity. Its total energy on reaching the earth is `6.27 xx 10^(n)J`. What is the value of `n`? Given, radius of earth is `6400 km` and `g = 9.8 m//s^(2)`. Air friction is neglected.

Answer 1

Correct Answer - `(9)`
A body projected upwards with escape speed will go to infinity. Thus, the speed of the body falling on earth from infinity will be equal to the escape speed to the earth which is given by
`upsilon_(e) = sqrt(2 gR) = sqrt(2 xx 9.8 xx 6400 xx 10^(3))`
`= 11.2 xx 10^(3) m//s`
`K.E.` acquired by body `= (1)/(2) m upsilon_(e)^(2)`
`= (1)/(2) xx 100 xx (11.2 xx 10^(3))^(2) = 6.27 xx 10^(9) J`
As per question, `6.27 xx 10^(n) = 6.27 xx 10^(9)`
so `n = 9`