A cylindrical vessel of $40$ cm radius is completely filled with water and its capacity is $528\ \text{dm}^3$ (dm : decimeter). The vessel is placed on a solid block of exactly same height as vessel. If a small hole is made at $70$ cm below the top of water level, then horizontal range of water falling on the ground in the beginning is ______ cm.
Answer: (B) $140\sqrt{2}$
Concept. Efflux speed $v=\sqrt{2gh}$ at depth $h$ below the surface; then the water is a horizontal projectile. Range $=2\sqrt{h\,H}$, with $H$ the hole's height above the ground.
Step 1. Vessel height. $V=\pi r^2H_v$: $0.528=\dfrac{22}{7}(0.16)H_v\Rightarrow H_v=1.05$ m; the block is also $1.05$ m.
Step 2. Hole. $h=0.70$ m below the surface; height above the ground $=2.10-0.70=1.40$ m.
Step 3. Range. $2\sqrt{0.70\times1.40}=2\sqrt{0.98}=1.4\sqrt2$ m $=140\sqrt2$ cm.
Answer. Option B.
Solution by Sreeraj P, M.Sc Physics
