A body of density d is conuterpoised 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)/(2))`
C. `M (1 - (d)/(d_1))`
D. `(M(1 - d//d_2))/((1- d//d_1))`

Answer

D

Explanation

(d) Let `M_0 =` mass of body in vacuum. Apperent weight of the body in air =Apparent weight of standerd weight in air `rArr` Actual weight - upthrust due to displaced air = Actual weight - upthrust due to displaced air
`rArr M_0g - ((M_0)/(d_1))dg = Mg -((M)/(d_2))dg`
`rArr M_0 = (M[(1-(d)/(d_2)])/([1 -(d)/(d_1)])`