Question

The capacity of an RD bottle is $100cc$ and its mass is $45g.$ Find the mass of the bottle when it is filled with a liquid of density $600kg/{m^3}.$

Answer 1

Hint: The density of a body or material is given by the ratio of mass of that body or material with volume of body or material. The mass of bottle after adding liquid will increase by the mass of liquid added in it

Complete step by step answer:
Let the mass and volume of the bottle are ${M_b}$and ${V_b}$respectively, then it is given that
\[\left. {M_b} = 45g \\ {V_b} = \ ,100c{m^3} \\\right].........\left( i \right)\]
Now, the bottle is filled with a liquid of density \[600kg/{m^3}.\] The above data [equation] are given in gram(g) and cc\[\left[ {c{m^3}} \right]\], so we convert the density of liquid in gram per centimeter cube $\left[ {g/c{m^3}} \right]$.
As we know,
$1kg\, = \,1000g$and $1metre\, = \,100cm$
So, the density of liquid is given by gram per cc, let the density is denoted by symbol ${\rho _L}$so
$
  {\rho _L} = 600kg/{m^3} \\
   = 600 \times \dfrac{{1000gram}}{{100cm \times 100cm \times 100cm}} \\
 $
$
   = \dfrac{6}{{10}}g/c{m^3} \\
  {\rho _L} = 0.6g/c{m^3} \\
   = 0.6g/cc \\
 $
Now the mass of the liquid say ${M_\ell }$is given by ${M_\ell } = {\rho _L}\,{V_L}\,..........\left( {ii} \right)$
Because the bottle is filled full with liquid of same volume,
so, \[{V_L} = {V_b} = 100c{m^3}\left[ {given} \right]\]
From the equation (ii) mass of the liquid, $
  {M_\ell } = 0.6 \times 100 \\
  {M_\ell } = 60gram \\
 $

Now, the bottle was already weighing $40g$before filling it with liquid.
So, after filling by the liquid into the bottle now,
Total mass of Bottle $ = $mass of bottle when empty $ + $mass of liquid when filled
$ = 40g + 60g$
$ = 100g.$

Note:
The density of a body is a liquid is given by product of mass and volume of that body or liquid in which the liquid is carried. Let's consider the density of the body and “V” then mass “M” of the body is given by $M = \rho \times V$.The mass of liquid will be the volume of bottle × density of liquid because the volume occupied by liquid in a bottle is the volume of bottle.