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A body of mass 716 g and volume 448 cm³ is put in liquid of density 1.3 g cm⁻³. Will It float or sink?

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Last updated date: 29th Feb 2024
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IVSAT 2024
Answer
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Hint: First calculate the weight of the body and then the buoyant force acting on it (that is equal to the weight of liquid displaced by the body). Then compare both of these values.
When the weight of the body is less than the buoyant force then it floats and if its weight is greater than the buoyant force then it sinks.
Formula for buoyant force (F): - $ F=V\rho g $ ,
Where V and ρ are the Volume of the liquid displaced and density of the liquid respectively.

Complete step by step answer
Given, mass of the body= 716 gram
Volume of the body= 448 cm³
Density of the given liquid = 1.3 g cm⁻³
 $ \begin{align}
  & Weight\text{ }of\text{ }the\text{ }body\text{ }=\text{ }mg\text{ }=\text{ }716\times g\text{ }...........\text{(A)} \\
 & \text{The buoyant force acting on the body is equal to weight of the liquid displaced by the body}\text{.} \\
 & \text{Thus, buoyant force (F)=V}\rho \text{g} \\
 & \text{ (where V=volume of the liquid displaced;} \\
 & \text{ }\rho \text{= density of the liquid)} \\
 & \text{Using above formula , F = 448}\times \text{1}\text{.3}\times \text{g = 582}\text{.4}\times \text{g }.............\text{(B) } \\
\end{align} $
From equations (A) and (B), since weight of the body given is greater than the buoyant force acting on it (i.e. W>F), therefore the body will sink.
Additional information: -Formula for weight of the liquid displaced by a body (or buoyant force) can be derived as: -
 $ \begin{align}
  & \text{We know that , weight (W) = mg }..........\text{(1)} \\
 & \text{and mass (m)= density(}\rho \text{)}\times \text{Volume(V) }..........\text{(2)} \\
 & \text{substituting (2) in (1), gives} \\
 & \text{W=V}\rho \text{g} \\
\end{align} $

Note
When a body is immersed partially or wholly in a liquid, then the various forces acting on the body are the upward thrust or buoyant force (F) and the weight of the body (W).
When W> F, the body will sink in the liquid;
(b) When W = F, then the body will remain in equilibrium inside the liquid;
(c) When W Buoyant force: -It is the force caused by the differences in pressure acting on opposite sides of an object immersed in a static fluid.

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