Two solid pieces, one of gold and the other of silver when immersed completely in water have equal weights. When weighted in air:

Options

A. the gold piece `(rho_(gold) lt rho_(silver))` will weigh more than silver
B. the silver piece will weigh more than gold
C. they will have the same weight
D. both of them weigh less than they weighed in water

Answer

B

Explanation

Suppose weight of gold in air = x g
weight of silver in air = `y g`
Density of gold = `d_(1)`
Density of silver = d_(2) (where d_(1) gt d_(2)`)
Volume of gold = (x)/(d_1), volume of silver = `(y)/(d_2)`
As weight of gold in water = weigth of silver in water
`(x-(x)/(d_1)xx1) g = (y-(x)/(d_2)xx1)g`
`=x/y = ((1-(1)/(d_2)))/((1-(1)/(d_1))) lt 1 or x lt y or y gt x`
i.e., weight of silver in air is more than that of gold in air.