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A body of density d is counterpoised by ...

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

A

`M`

B

`M(1-(d)/(d_(2)))`

C

`M(1-(d)/(d_(1)))`

D

`(M(1-d//d_(2)))/((1-d//d_(1)))`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `M_(0)` = mass of body in vacuum.
Apparent weight of the body in air = Apparent weight of standard weights in air implies Actual weight - upthrust due to displaced air = Actual weight - upthrust due to displaced air
`implies M_(0)g-((M_(0))/(d_(1)))dg = Mg-((M)/(d_(2)))dg implies M_(0) = (M[1-(d)/(d_(2))])/([1-(d)/(d_(1))])`
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