A cubical block of density `rho` is floating on the surface of water. Out of its height L, fraction x is submerged in water. The vessel is in an elevator ac celerating upward with ac celeration a. What is the fraction immersed ?

Explanation

Let `rho_w` be the density of water , volume of block, `V = L^3.` Mass of block, `m =V rho = L^3 rho` Let l be the height of iceberg submerged in water. Volume of iceberg in water `= l xx L^2 :.` Weight of water displaced by iceberg `= lL^2 xx rho_wg` Weight of block of ice berg ` = L^3 rho g` As iceberg is floating, so weight of iceberg = weight of water displaced by iceberg `L^3 rho g = IL^2 rho_w g or (I)/(L) = (rho)/(rho_w) =x (given)`
When vessel is in an elevator which is ac celerating upwards with ac celeration a, then effective weight of block = m(g + a). Let fraction of block `x_1` be submerged into water when elevator is ac celerating upwards. Since block is floating in the water, so `m (g + a ) = (x_1 L^3) rho_w (g+a) or x_1 = (m)/(L^3 rho_w) = (L^3 rho)/(L^3 rho_w) = (rho)/(rho_w) = x` It meas, the fraction of the block submerged is independent of any ac celeration of elevator.