A body of density d is counterpoised by Mg of weights of density `d_1` in air of density d. Then the true mass of the body is

Options

A. M
B. `M(1 (d)/(d_2))`
C. `M(1 - (d)/(d_1))`
D. `(M(1 - d//d_2))/((1 - d//d_1))`

Answer

D

Explanation

`d_1 Vg -dVg = Mg - (d)/(d_2) Mg`
`(d_1 - d) V = M (1 - (d)/(d_2))`
`V = (M(1 - d//d_2))/((d_1 - d))`
Mass of body `= d_1 V = (d_1(1 - d//d_2))/((d_1 - d))M`
=`(M(1 - d//d_2))/((1 - d//d_1))`.
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