A tank has a small hole of area A at depth H. A disk initially seals the hole with pressure force F. When disk is moved slightly away, water jets out and strikes the disk inelastically. If jet force is NF/4, find N. [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

A tank has a small hole of area A at depth H. A disk initially seals the hole with pressure force F. When disk is moved slightly away, water jets out and strikes the disk inelastically. If jet force is NF/4, find N. [See Image.]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — Static force on plate sealing hole of area A at depth H is F = ρgHA. Step 2 — When the hole is opened, Torricelli speed v = √(2gH). Mass flow rate ṁ = ρAv. Step 3 — Water striking disk inelastically loses axial velocity v, so momentum flux force is Fⱼₑₜ = ṁv = ρAv² = 2ρgHA = 2F. Step 4 — With force expressed as NF/4, N/4 = 2 ⇒ N = 8.