A wooden block floats in a liquid with 40% of its volume inside the liquid. When the vessel containing the liquid starts rising upwards with acceleration a = g/2, the percentage of volume inside the liquid is :

Options

A. 0.2
B. 0.6
C. 0.3
D. 0.4

Answer

D

Explanation

When the vessel is stationary, weight of the wooden block is balanced by the upthrust, that is `V_(p_("wood")) g = V_("liq") P_("liq")` g, where V is the volume of the block and Vuq is the volume of liquid displaced, `p_("wood")` and `P_("liq")` are the densities of wood and liquid respectively. This gives `V_("liq"//V) = (p_("wood")//P_("liq"))`· When the vessel moves up, the net upward force is (upthrust-weight). The upthrust is `[V_("liq") P_("liq")g]` where `(V_("liq")` is the volume of the liquid displaced in this case. The net upward force is `[VP_("wood")` g/2`]`. This gives `[V_("liq").//V = P_("wood")//P_("liq")]`. From this we see that the same volume of the wooden block remains inside the liquid.
Thus correct choice is (d).