A body is thrown vertically up with certain initial velocity, the potential and kinetic energies of the body are equal is thrown with double the velocity upwards, the ratio of potential and kinetic energies upwards, the ratio of potential and kinetic energies of the body when it crosses the same point, is

Options

A. `1 : 1`
B. `1 : 4`
C. `1 : 7`
D. `1 : 8`

Answer

`(3)`

Explanation

In first case, at .P., `TE = PE + KE = 2PE and TE_("bottom") = 1/2 mu^(2)`
In second case,
`TE_(bottom)^(1) = 1/2m(2u)^(2) = 4TE = 8PE `
AT `P`,` (PE^(1))/(KE_(1)) = (PE^(1))/(TE^(1) - PE^(1))= PE /(8PE - PE)`