A spherical air bubble is rising from the depth of a lake when pressure is `P atm` and temperature is `T K`. The percentage increase in the radius when it comes to the surface of a lake will be (Assume temperature and pressure at the surface to be, respectively, `2T K` and `P//4`.)

Options

A. `100%`
B. `50%`
C. `40%`
D. `200%`

Answer

A

Explanation

`(P_(1)V_(1))/(T_(1)) = (P_(2)V_(2))/(T_(2)) , V_(1) =` initial volume, `V_(2) =` final volume
`(P V_(1))/(T) = (P)/(4) xx (V_(2))/(2T)`
`V_(1) = (V_(2))/(8)`
`V_(2) = 8V_(1)`
`V_(2) = 8 xx (4)/(3) pi ^(3) = (4)/(3) pi (8r)^(3)`
New radius `= 2r` ( `:.` 100% radius will increase)