Question

A denisty of a bottle weighs 0.25N when empty & 0.75N when filled with water & 0.65N when filled with alcohol. Calculate;. 1) the volume of the bottle 2) the denisty of the alcohol (denisty of water is 1000kg/m & g is 10m

Answer 1

Answer:

$0.05\times 10^{-3}\ \text{m}^3$

$800\ \text{kg/m}^3$

Explanation:

$W_b$ = Weight of bottle = 0.25 N

$W_w$ = Weight of water = $0.75-0.25=0.5\ \text{N}$

g = Acceleration due to gravity = $10\ \text{m/s}^2$

$\rho_w$ = Density of water = $1000\ \text{kg/m}^3$

Mass of water

$m_w=\dfrac{W_w}{g}\\\Rightarrow m_w=\dfrac{0.5}{10}\\\Rightarrow m_w=0.05\ \text{kg}$

Volume is given by

$V_w=\dfrac{m_w}{\rho_w}\\\Rightarrow V_w=\dfrac{0.05}{1000}\\\Rightarrow V_w=0.05\times 10^{-3}\ \text{m}^3$

Volume of the bottle is $0.05\times 10^{-3}\ \text{m}^3$.

This means that the alcohol will take the same amount of volume.

$W_a$ = Weight of alcohol = $0.65-0.25=0.4\ \text{N}$

Mass of alcohol

$m_a=\dfrac{0.4}{10}\\\Rightarrow m_a=0.04\ \text{kg}$

Density is given by

$\rho=\dfrac{m_a}{V_w}\\\Rightarrow \rho=\dfrac{0.04}{0.05\times 10^{-3}}\\\Rightarrow \rho=800\ \text{kg/m}^3$

Density of alcohol is $800\ \text{kg/m}^3$