Spheres of iron and lead having same mass are completely immersed in water . Density of lead is more than that of iron . Apparent loss of weight is `W_(1)` for iron sphere and `W_(2)` for lead sphere . Then `(W_(1))/(W_(2))` is

Options

A. `=1`
B. between 0 and 1
C. `= 0`
D. `gt 1`

Answer

D

Explanation

Density `(rho) = ("Mass (M)")/("Volume (V)")`
`p prop (1)/(V)` For the same mass .
`therefore (rho_("lead"))/(rho_("iron")) = (V_("iron"))/(V_("lead"))`
As `rho_("lead") gt rho_("iron")` (Given)
`therefore (V_("iron"))/(V_("lead")) gt 1 " " ... (1)`
Using law of floatation ,
For iron sphere
`W_(1) = V_("iron") rho_("water") g " " .... (ii)`
For lead sphere
`W_(2) = V_("lead") rho_("water") g " " .... (iii)`
Divide (ii) by (iii) , we get
`(W_(1))/(W_2) = (V_("iron"))/(V_("lead")) gt 1 " " ` (Using (i))