Question

(a) `A` spherical tank of `1.2m` radius is half filled with oil of relaive density `0.8`. If the tank is given a horizontal acceleration of `10m//s^(2)`. Calculate the inclination of the oil surface to horizontal and maximum pressure on the tank.
(b) The volume of an air bubble is doubled as it rises from the bottom of a lake to its surface. If the atmospheric pressure is `H m` of mercury `&` the density of mercury is `n` times that of lake water. Find the depth of the lake.

Answer 1

Correct Answer - `(a) 9600sqrt(2)N//m^(2) " "(b)nH`
(a) `P_(max) = h.rho.g_(eff)`
`P_(max) = 1.2xx800xxsqrt(2)xx10`
`P_(max) = 9600sqrt(2) N//m^(2)`

(b)`P_(1)V_(1) = P_(2)V_(2)`
`(P+hrho_(w)g)V=P(2V)`
`hrho_(w)g=P`
`hrho_(w)g = Hrho_(Hg)g`
`hrho_(w) = H(nrho_(w))`
`h=nH`