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If the volume of a substance is $20 {cm}^{3}$ and have mass $50 g$ then find the correct relation/s if the density of water is $1 g {cm}^{- 3}$ ?

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The density of the substance is greater than the density of the water

The substance will sink into the water

Buoyant force by water is less than the weight of the substance

All of the above

answer is D.

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Detailed Solution

If the volume of a substance is

20 {cm}^{3}

and have mass

50 g

then the Density of substance is greater than the density of water, hence the substance will sink in water and weight of the substance is greater than the buoyant force by water.
Given that the volume of substance is

20 {cm}^{3}

.
Mass of substance

= 50 g

Then the density of the substance

ρ_{substance} = \frac{mass}{volume}

\Rightarrow ρ_{substance} = \frac{50 g}{20 c m^{3}}

\Rightarrow ρ_{substance} = 2.5 g / {cm}^{3}

Hence the density of the substance is greater than the density of water; hence substance will sink. The buoyant force exerted by water

B = V ρ_{water} g

Here

V

is the volume of substance,

ρ_{water}

is the density of water and

g

is the acceleration due to gravity.
Water has density

ρ_{water} = 1 g / {cm}^{3}

which is less than the density of substance

ρ_{substance} = 2.5 g / {cm}^{3}

This buoyancy force by water is less than the weight of the substance and hence the substance will sink.

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