Question

3. If a substance of mass 25 g has a volume of 10 cm^3, its density is:=
a. 2500 kg/m^3.
b. 2.5 kg/m^3.
c. 2500 g/cm^3.
d. 250 g/cm^3.

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Answer 1

Answer :-

Density of the substance is 2500 kg/m³ [Option.a]

Explanation :-

We have :-

→ Mass of the substance = 25 g

→ Volume = 10 cm³

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From the existing options, we can understand that we have to calculate density of the substance in kg/m³.

Firstly, let's convert mass of the substance from g to kg and volume of the substance from cm³ to m³.

Mass :-

⇒ 1 g = 0.001 kg

⇒ 25 g = 25(0.001)

⇒ 0.025 kg

Volume :-

⇒ 1 cm³ = 10⁻⁶ m³

⇒ 10 cm³ = 10(10⁻⁶)

⇒ 10⁻⁵ m³

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Density = Mass/Volume

⇒ Denisty = 0.025/10⁻⁵

⇒ Density = 0.025 × 10⁵

⇒ Denisty = 0.025 × 100000

⇒ Density = 2500 kg/m³

Answer 2

Answer:

Given :-

• A substance of mass 25 g has a volume of 10 cm³.

To Find :-

• What is the density of a substance.

Formula Used :-

$\clubsuit$ Density Formula :

$\longmapsto \sf\boxed{\bold{\pink{\rho =\: \dfrac{m}{v}}}}$

where,

• ρ = Density
• m = Mass
• v = Volume

Solution :-

First, we have to convert mass g to kg :

$\implies \sf Mass =\: 25\: g$

$\implies \sf Mass =\: \dfrac{25}{1000}\: kg\: \: \bigg\lgroup \sf\bold{1\: g =\: \dfrac{1}{1000}\: kg}\bigg\rgroup$

$\implies \sf\bold{\purple{Mass =\: 0.025\: kg}}$

Again, we have to convert volume cm³ to m³ :

$\implies \sf Volume =\: 10\: cm^3$

$\implies \sf Volume =\: 10 \times 10^{- 6}\: m^3$

$\implies \sf\bold{\purple{Volume =\: 10^{- 5}\: m^3}}$

Now, we have to find the density of a substance :

Given :

$\bigstar\: \: \sf Mass =\: 0.025\: kg$

$\bigstar\: \: \sf Volume =\: 10^{- 5}\: m^3$

According to the question by using the formula we get,

$\longrightarrow \sf \rho =\: \dfrac{0.025}{10^{- 5}}$

$\longrightarrow \sf \rho =\: 0.025 \times 10^5$

$\longrightarrow \sf \rho =\: \dfrac{25}{1000} \times 10 \times 10 \times 10 \times 10 \times 10$

$\longrightarrow \sf \rho =\: \dfrac{25}{1000} \times 100000$

$\longrightarrow \sf \rho =\: \dfrac{2500\cancel{000}}{1\cancel{000}}$

$\longrightarrow \sf \rho =\: \dfrac{2500}{1}$

$\longrightarrow \sf\bold{\red{\rho =\: 2500\: kg/m^3}}$

$\therefore$ The density of a substance is 2500 kg/m³.

Hence, the correct options is option no (a) 2500 kg/m³.