An object weights `m_(1)` in a liquid of density `d_(1)` and that in liquid of density `d_(2)` is `m_(2)`. The density of the object is

Options

A. `(m_(2)d_(2)-m_(1)d_(1))/(m_(2)-m_(1))`
B. `(m_(1)d_(1)-m_(2)d_(2))/(m_(2)-m_(1))`
C. `(m_(2)d_(1)-m_(1)d_(2))/(m_(1)-m_(2))`
D. `(m_(1)d_(2)-m_(2)d_(1))/(m_(1)-m_(2))`

Answer

D

Explanation

Given that an object weights `m_(1)` in a liquid of density `d_(1)` and `m_(2)` in a liquid of density `d_(2)` so when the density of the object is d, then we get
`V(d-d_(1))=m_(1)" and "V(d-d_(2))=m_(2)`
`"Thus, "(d-d_(1))/(d-d_(2))=m_(1)/m_(2)`
`"So, we get "d=(m_(1)d_(2)-m_(2)d_(1))/(m_(1)-m_(2))`