A wire of radius `r`, Young's modulus `Y` and length `l` is hung from a fizxed point and support a heavty metal cycliner of volume `V` at its own lowest end. The change in length of the wire when cyclinder is immersed in a liquid of density `rho`, is in fact

Options

A. decreases by `(Vl rho g)/(Y pi r^(2))`
B. increses by `(V r rho g)/(Y pi l^(2))`
C. decreaes by `(V rho g)/(Y pi r)`
D. increaes by `(V rho g)/(pi r l)`

Answer

A

Explanation

`Mg = (Y pi r^(2))/(l) Delta l = W.....(1), W' = (Y pi r^(2))/(l) Delta l,.......(2)`
`therefore W - W' = (Y pi r^(2))/(l) (Delta l - Delta l'), Delta l - Delta l' = (V rho g l)/(Y pi r^(2))`