A wooden piece can float both in mercury (of density 13.6 g/cc ) and in water (of density 1 gm/cc ). The ratio of mass of mercury displaced to the mass of water displaced is

Question

A wooden piece can float both in mercury (of density 13.6 g/cc ) and in water (of density 1 gm/cc ). The ratio of mass of mercury displaced to the mass of water displaced is (A)  1  (B)  13.6  (C)  (1/13.6)  (D)  (12.6/13.6)

Tardigrade Admin · Accepted Answer

If the same body is made to float in different liquids of density σA and σB respectively. VP=(Vm)A σA=(Vm)B σB ∴ (mA/mB)=1

Q. A wooden piece can float both in mercury (of density $13.6 g / cc$ ) and in water (of density $1 g m / cc$ ). The ratio of mass of mercury displaced to the mass of water displaced is

$1$

$13.6$

$\frac{1}{13.6}$

$\frac{12.6}{13.6}$

If the same body is made to float in different liquids of density $σ_{A}$ and $σ_{B}$ respectively.
$V_{P} = (V_{m})_{A} σ_{A} = (V_{m})_{B} σ_{B}$
$∴ \frac{m _{A}}{m _{B}} = 1$

Q. A wooden piece can float both in mercury (of density 13.6g/cc ) and in water (of density 1gm/cc ). The ratio of mass of mercury displaced to the mass of water displaced is

1

13.6

13.61​

13.612.6​

If the same body is made to float in different liquids of density σA​ and σB​ respectively. VP​=(Vm​)A​σA​=(Vm​)B​σB​ ∴mB​mA​​=1

Q. A wooden piece can float both in mercury (of density $13.6 g / cc$ ) and in water (of density $1 g m / cc$ ). The ratio of mass of mercury displaced to the mass of water displaced is

$1$

$13.6$

$\frac{1}{13.6}$

$\frac{12.6}{13.6}$

If the same body is made to float in different liquids of density $σ_{A}$ and $σ_{B}$ respectively.
$V_{P} = (V_{m})_{A} σ_{A} = (V_{m})_{B} σ_{B}$
$∴ \frac{m _{A}}{m _{B}} = 1$