Question

A container open from top, filled with water (density $\rho$) 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 in the given two arrangements. In arrangement - 1, the ball is connected by a rigid rod (of negligible volume) and held in the water with a force enough for it to not come up or move. In arrangement - 2, the ball is attached with bottom by a massless string. Choose the incorrect option with regard to the reading of weighing machine. (density of wood is less than water)

• A. In arrangement - 1 reading is W.
• B. In arrangement - 1 reading is $W+\rho Vg$.
• C. In arrangement - 2 reading is $W+mg-\rho Vg$.
• D. In arrangement - 2 reading is less than that in arrangement - 1.

Answer 1

The correct option is B In arrangement - 1 reading is $W+\rho Vg$.

(1) In arrangement - 1, water of weight $\rho Vg$ has come out, but the buoyancy force is equal to the weight of displaced liquid. So, reading of weighing machine is W.
New reading $=$ W$-$(weight of water displaced)+weight of ball+force exerted on rod $=W+mg-\rho Vg+N=W+mg-\rho Vg-mg+\rho Vg=W$
(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 $W+mg-\rho Vg$.