Ncert Exercises & Solutions

The mass and volume of a body are $4.237~\text{grams}$ and $2.5~\text{cm}^3,$ respectively. The density of the material of the body in correct significant figures will be:
1. $1.6048~\text{grams cm}^{-3}$
2. $1.69~\text{grams cm}^{-3}$
3. $1.7~\text{grams cm}^{-3}$
4. $1.695~\text{grams cm}^{-3}$

Hint: Use the concept of measuring the significant figures.

Step 1: Find the density of the body.

In this question, density should be reported to two significant figures.
The density of the material is given by;

\Rightarrow Density = \frac{Mass}{Volume}

$\Rightarrow \text{Density}=\frac{\text{Mass}}{\text{Volume}}$

\Rightarrow Density = \frac{4.237 g}{2.5 {c m}^{3}} = 1.6948 g {c m}^{- 3}

$\Rightarrow \text { Density }=\frac{4.237 \mathrm{~g}}{2.5 \mathrm{~cm}^3}=1.6948 \mathrm{~g} \mathrm{~cm}^{-3}$

Step 2: Round off the value to the appropriate significant figures.

The result should have as many significant figures as there are in the value with the least significant figures.

As rounding off the number, we get the density

ρ = 1.7 g c m^{- 3}

$\rho=1.7~\mathrm{g~cm^{-3}}$

Therefore, the density of the material is

1.7 g c m^{- 3} .

$1.7~\mathrm{g~cm^{-3}}.$
Hence, option (3) is the correct answer.

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