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Physics

Fluid-Mechanics

Easy

Question

A body of density d is counterpoised by M g of weights of density d₁ in air of density d. Then the true mass of the body is

M
$M (1 - \frac{d}{d_{2}})$
$M (1 - \frac{d}{d_{1}})$
$\frac{M (1 - d / d_{2})}{(1 - d / d_{1})}$

The correct answer is: $fraction numerator M open parentheses 1 minus d divided by d subscript 2 close parentheses over denominator open parentheses 1 minus d divided by d subscript 1 close parentheses end fraction$

Let M₀= mass of body in vacuum.
Apparent weight of the body in air = Apparent weight of standard weights in air
$rightwards double arrow$ Actual weight - upthrust due to displaced air
= Actual weight - upthrust due to displaced air
$table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell not stretchy rightwards double arrow M subscript 0 g minus open parentheses M subscript 0 over d subscript 1 close parentheses d g equals M g minus open parentheses M over d subscript 2 close parentheses d g end cell row cell not stretchy rightwards double arrow M subscript 0 equals fraction numerator M open square brackets 1 minus d over d subscript 2 close square brackets over denominator open square brackets 1 minus d over d subscript 1 close square brackets end fraction end cell end table$

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