Question

() The density of aluminium is 2.7 g cm and
of brass is 8-4 g cm. For the same mass,
the volume of:
(i) both will be same
(ii) aluminium will be less than that of brass
(iii) aluminium will be more than that of brass
(iv) nothing can be said.



with explanation please. ​

Answer 1

CORRECT QUESTION:

The density of Aluminium is 2.7 g/cm³ and of Brass is 8.4 g/cm³. For the same mass,the volume of:

• (i) both will be same
• (ii) Aluminium will be less than that of brass
• (iii) Aluminium will be more than that of brass
• (iv) nothing can be said.

ANSWER:

Option (iii) The volume of Aluminium will be more than that of brass.

DEFINITION:

Density is defined as the ratio of mass to the volume.

FORMULA:

$\bf{ \sf{\fbox{Denisty = \frac{Mass}{Volume } \implies Volume = \frac{Mass}{Density} }}}$

GIVEN:

$\rho_A = 2.7 g/cm^3 \\ \\ \rho_B = 8.4 g/cm^3 \\ \\ m_A = m_B = m$

EXPLANATION:

$\displaystyle \dfrac{V_A}{V_B} = \dfrac{ \dfrac{m_A}{ \rho_A} }{ \dfrac{m_B}{ \rho_B} } \\ \\ \\ \displaystyle \dfrac{V_A}{V_B} = \dfrac{ \dfrac{m}{ \rho_A} }{ \dfrac{m}{ \rho_B} } \\ \\ \\ \dfrac{V_A}{V_B} = \frac{ \rho_B}{ \rho_A} \\ \\ \\ \dfrac{V_A}{V_B} = \frac{8.4}{2.7} \\ \\ \\ \dfrac{V_A}{V_B} = \frac{28}{9} \\ \\ \\ \dfrac{V_A}{V_B} = 3.1 \\ \\ \\ V_A = 3.1V_B$

HENCE THE VOLUME OF ALUMINIUM WILL BE 3.1 TIMES OF BRASS.