1.

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 :

Answer»

0.2
0.6
0.3
0.4

Solution :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).


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