A container open from top, filled with water (density `rho_w`) upto the top, is placed on a weighing machine and the reading is W. A wooden ball of volume V and mass m is put in the water by the given two arrangements. In arrangement–1, the ball is connected by a rigid rod (of negligible volume) and pushed in the water. In arrange- ment–2, the ball is attached with bottom by a massless string. The reading of weighing machine, (density of wood is less than water) (choose incorrect option)

Options

A. In arrangement-1 is W
B. in arrangement -1 is `W+rhoVg`
C. In arrangement-2 is `W+mg-rho_(w)Vg`
D. In arragement-2 is less that in arragement -1

Explanation

(1) In arrangement -1, water of weight `rhoVg` gas come out, but the buyoancy force is also equal to the weight of displaced liquid. So, reading of weighing machine is W. (2) in arrangement-2, weight of the ball mg is added, but water of weight `rho_(w) Vg` is removed so reading of weighing machine is W+ mg -`rho Vg`.