Question

A long metal rod of length l and relative density σis held vertically with its lower end just touching the surface of water. The speed of the rod when it just sinks in water is given by

Answer 1

Answer:

root(2gl(1-1/σ))

Explanation:

mg - m'g = ma

therefore a=g(1-m'/m)             (where m/m'=σ)

since a=v(dv/dx)

therefore v(dv/dx)=g(1-1/σ)

Integrating we get:-

(v^2)/2=gl(1-1/σ)                      (integration of dx=l)

v^2=2gl(1-1/σ)  

v=root(2gl(1-1/σ))