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The mass of two objects are in the ratio $1 : 4$ and have equal volumes. Then the ratio of their densities will be?

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4 : 1

1 : 4

6 : 1

1 : 6

answer is B.

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Detailed Solution

The mass of two objects in the ratio

1 : 4

and have equal volumes. Then the ratio of their densities is

1 : 4

.
Let objects A and B have masses

M_{A}

and

M_{B}

with equal volumes

V

and have densities

d_{A}

and

d_{B}

respectively.
We know that the

mass = volume \times density

{\Rightarrow M}_{A} = V d_{A}

{\Rightarrow M}_{B} = V d_{B}

Given the ratios of masses

\frac{M_{A}}{M_{B}} = \frac{1}{4}

\Rightarrow \frac{M_{A}}{M_{B}} = \frac{V d_{A}}{V d_{B}}

\Rightarrow \frac{d_{A}}{d_{B}} = \frac{1}{4}

Hence the ratio of densities of two blocks

d_{A} : d_{B} = 1 : 4

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